Table 2- Factorizations of 2^n-1, n odd, n<1200 n Prime Factors 3 7 5 31 7 127 9 (3) 73 11 23.89 13 8191 15 (3,5) 151 17 131071 19 524287 21 (3,7) 7*.337 23 47.178481 25 (5) 601.1801 27 (3,9) 262657 29 233.1103.2089 31 2147483647 33 (3,11) 599479 35 (5,7) 71.122921 37 223.616318177 39 (3,13) 79.121369 41 13367.164511353 43 431.9719.2099863 45 (3,5,9,15) 631.23311 47 2351.4513.13264529 49 (7) 4432676798593 51 (3,17) 103.2143.11119 53 6361.69431.20394401 55 (5,11) 881.3191.201961 57 (3,19) 32377.1212847 59 179951.3203431780337 61 2305843009213693951 63 (3,7,9,21) 92737.649657 65 (5,13) 145295143558111 67 193707721.761838257287 69 (3,23) 10052678938039 71 228479.48544121.212885833 73 439.2298041.9361973132609 75 (3,5,15,25) 100801.10567201 77 (7,11) 581283643249112959 79 2687.202029703.1113491139767 81 (3,9,27) 2593.71119.97685839 83 167.57912614113275649087721 85 (5,17) 9520972806333758431 87 (3,29) 4177.9857737155463 89 618970019642690137449562111 91 (7,13) 911.112901153.23140471537 93 (3,31) 658812288653553079 95 (5,19) 191.420778751.30327152671 97 11447.13842607235828485645766393 99 (3,9,11,33) 199.153649.33057806959 101 7432339208719.341117531003194129 103 2550183799.3976656429941438590393 105 (3,5,7,15,21,35) 29191.106681.152041 107 162259276829213363391578010288127 109 745988807.870035986098720987332873 111 (3,37) 321679.26295457.319020217 113 3391.23279.65993.1868569.1066818132868207 115 (5,23) 14951.4036961.2646507710984041 117 (3,9,13,39) 937.6553.86113.7830118297 119 (7,17) 239.20231.62983048367.131105292137 121 (11) 727.1786393878363164227858270210279 123 (3,41) 3887047.177722253954175633 125 (5,25) 269089806001.4710883168879506001 127 170141183460469231731687303715884105727 129 (3,43) 11053036065049294753459639 131 263.10350794431055162386718619237468234569 133 (7,19) 163537220852725398851434325720959 135 (3,5,9,15,27,45) 271.348031.49971617830801 137 32032215596496435569.5439042183600204290159 139 5625767248687.123876132205208335762278423601 141 (3,47) 4375578271.646675035253258729 143 (11,13) 724153.158822951431.5782172113400990737 145 (5,29) 2679895157783862814690027494144991 147 (3,7,21,49) 7*.2741672362528725535068727 149 86656268566282183151.8235109336690846723986161 151 18121.55871.165799.2332951.7289088383388253664437433 153 (3,9,17,51) 919.75582488424179347083438319 155 (5,31) 31*.311.11471.73471.4649919401.18158209813151 157 852133201.60726444167.1654058017289.2134387368610417 159 (3,53) 6679.13960201.540701761.229890275929 161 (7,23) 1289.3188767.45076044553.14808607715315782481 163 150287.704161.110211473.27669118297.36230454570129675721 165 (3,5,11,15,33,55) 2048568835297380486760231 167 2349023.79638304766856507377778616296087448490695649 169 (13) 4057.6740339310641.3340762283952395329506327023033 171 (3,9,19,57) 93507247.3042645634792541312037847 173 730753.1505447.70084436712553223.155285743288572277679887 175 (5,7,25,35) 39551.60816001.535347624791488552837151 177 (3,59) 184081.27989941729.9213624084535989031 179 359.1433.1489459109360039866456940197095433721664951999121 181 43441.1164193.7648337.7923871097285295625344647665764672671 183 (3,61) 367.55633.37201708625305146303973352041 185 (5,37) 1587855697992791.7248808599285760001152755641 187 (11,17) 707983.1032670816743843860998850056278950666491537 189 (3,7,9,21,27,63) 1560007.207617485544258392970753527 191 383.7068569257.39940132241.332584516519201.87274497124602996457 193 13821503.61654440233248340616559.14732265321145317331353282383 195 (3,5,13,15,39,65) 134304196845099262572814573351 197 7487.26828803997912886929710867041891989490486893845712448833 199 164504919713.4884164093883941177660049098586324302977543600799 201 (3,67) 1609.22111.87449423397425857942678833145441 203 (7,29) 136417.121793911.11348055580883272011090856053175361113 205 (5,41) 2940521.70171342151.3655725065508797181674078959681 207 (3,9,23,69) 79903.634569679.2232578641663.42166482463639 209 (11,19) 94803416684681.1512348937147247.5346950541323960232319657 211 15193.60272956433838849161.3593875704495823757388199894268773153439 213 (3,71) 66457.2849881972114740679.4205268574191396793 215 (5,43) 1721.731516431.514851898711.297927289744047764444862191 217 (7,31) 5209.62497.6268703933840364033151.378428804431424484082633 219 (3,73) 3943.671165898617413417.4815314615204347717321 221 (13,17) 1327.2365454398418399772605086209214363458552839866247069233 223 18287.196687.1466449.2916841.1469495262398780123809.P24 225 (3,5,9,15,25,45,75) 115201.617401.1348206751.13861369826299351 227 26986333437777017.P52 229 1504073.20492753.59833457464970183.P39 231 (3,7,11,21,33,77) 463.P34 233 1399.135607.622577.P57 235 (5,47) 2391314881.72296287361.P35 237 (3,79) 1423.49297.23728823512345609279.31357373417090093431 239 479.1913.5737.176383.134000609.P49 241 22000409.P66 243 (3,9,27,81) 487.16753783618801.192971705688577.3712990163251158343 245 (5,7,35,49) 1471.P48 247 (13,19) 15809.6459570124697.402004106269663.P34 249 (3,83) 1621324657.P40 251 503.54217.178230287214063289511.61676882198695257501367.P26 253 (11,23) 23*.4103188409.199957736328435366769577.P32 255 (3,5,15,17,51,85) 106591.949111.P28 257 535006138814359.1155685395246619182673033.P39 259 (7,37) 2499285769.P56 261 (3,9,29,87) P51 263 23671.13572264529177.120226360536848498024035943.P36 265 (5,53) 29324808311.197748738449921.P38 267 (3,89) 78903841.28753302853087.P32 269 13822297.P74 271 15242475217.P72 273 (3,7,13,21,39,91) 108749551.4093204977277417.86977595801949844993 275 (5,11,25,55) 382027665134363932751.P40 277 1121297.31133636305610209482201109050392404721.P40 279 (3,9,31,93) 16183.34039.1437967.833732508401263.2034439836951867299888617 281 80929.P80 283 9623.68492481833.P71 285 (3,5,15,19,57,95) 1491477035689218775711.25349242986637720573561 287 (7,41) 17137716527.P62 289 (17) 12761663.179058312604392742511009.P52 291 (3,97) 272959.2065304407.5434876633.P34 293 40122362455616221971122353.P63 295 (5,59) 4721.132751.5794391.128818831.3812358161.452824604065751.P22 297 (3,9,11,27,33,99) 8950393.P48 299 (13,23) 599.9341359.14718679249.13444476836590589479. .51441563151591093599.260242449712509916159 301 (7,43) 490631.365505823711978039310711.P47 303 (3,101) 607.P58 305 (5,61) 1831.2441.4271.270841.484074637694471.P42 307 14608903.85798519.23487583303.78952752017.P57 309 (3,103) 1953272766780718501831.P40 311 5344847.2647649373910205158468946067671.P57 313 10960009.14787970697180273.3857194764289141165278097.P47 315 (3,5,7,9,15,21,35,45,63,105) 870031.983431.P32 317 9511.587492521482839879.4868122671322098041565641.P49 319 (11,29) 18503.64439.84819793631.P64 321 (3,107) 17866285599391.P51 323 (17,19) 647.7753.39044358788825633753.P61 325 (5,13,25,65) 7151.51879585551.P58 327 (3,109) 20597276734348736647.33157029794959983067039.P23 329 (7,47) 12503.200033.9106063.270447871.P58 331 16937389168607.865118802936559.P72 333 (3,9,37,111) 1999.10657.169831.1238761.36085879.199381087. .698962539799.4096460559560875111 335 (5,67) 464311.1532217641.P65 337 18199.2806537.95763203297.726584894969.P68 339 (3,113) 10113049.320021624768405574452943847.P34 341 (11,31) 5560125493425335999.126901141805369975317583.P49 343 (7,49) 6073159.1428389887.62228099977.P62 345 (3,5,15,23,69,115) P54 347 14143189112952632419639.P83 349 1779973928671.34720396273212657799920861294559.P62 351 (3,9,13,27,39,117) 446473.29121769.571890896913727.93715008807883087.P21 353 931921.2927455476800301964116805545194017.P67 355 (5,71) 121932688511.P73 357 (3,7,17,21,51,119) 4999.245262248913715001137177.P31 359 719.855857.778165529.65877330027880703. .370906580744492785430299503112990447.P39 361 (19) 9522401530937.36450568206770608791178096385783.P59 363 (3,11,33,121) 8713.7593961.75824014993.P45 365 (5,73) 8761.13828603741081.82595052745831.P56 367 12479.51791041.78138581882953.301311116540899114446723859201.P56 369 (3,9,41,123) 6376386802464073.P57 371 (7,53) 743.2969.63781899287.204712366597949333831.P57 373 25569151.P105 375 (3,5,15,25,75,125) 751.P58 377 (13,29) 5279.148055441.359661017.P81 379 180818808679.P103 381 (3,127) 2287.15241.349759.P63 383 1440847.7435494593.503823044204581129045587727. .15174923558680812616818436353130417.P39 385 (5,7,11,35,55,77) 55441.1971764055031.P56 387 (3,9,43,129) 11492353.22763003975641.6834040335349578249140287.P31 389 56478911.4765678679.P100 391 (17,23) 37537.25806248225716242845491832244899635927231330561.P55 393 (3,131) 36093121.51118297.58352641.P55 395 (5,79) 12641.5435488351.16203007441.P70 397 2383.6353.50023.53993.202471.5877983. .814132872808522587940886856743.1234904213576000272542841146073.P31 399 (3,7,19,21,57,133) 73417.83791.P56 401 856971565399.2136958965524920285681. .594538100848945223169882301931953.P55 403 (13,31) 45137.8532838289.P94 405 (3,5,9,15,27,45,81,135) 537841.11096527935003481.P44 407 (11,37) 3257.3068001817.1826375940722234754636475033.P68 409 4480666067023.76025626689833.P97 411 (3,137) 823.27261904199932321.647923469936355993348337.P39 413 (7,59) 2006647231.6774027833473375976915021445395839.P62 415 (5,83) 470933694191.3028917598961.130666175908831. .32367218471375835379289471.P35 417 (3,139) 7606017793609.P70 419 839.903780021613921.5800422716722833271214743. .10287968884341772230096159036619433593.P47 421 614002928307599.P112 423 (3,9,47,141) 1617189999730415801728461273583.P53 425 (5,17,25,85) P97 427 (7,61) 33282089.P101 429 (3,11,13,33,39,143) 17286204937.1065107717756542892882802586807.P33 431 863.3449.36238481.76859369.558062249.4642152737. .142850312799017452169.P70 433 22086765417396827057.737748363812546584876297. .5028667832511715101284999.P63 435 (3,5,15,29,87,145) 256582225885581001782477601.P42 437 (19,23) 3198841.5579617.6203145044672921.P90 439 104110607.127321491658223.122551752733003055543.P90 441 (3,7,9,21,49,63,147) 126127.309583.5828257.4487533753346305838985313.P34 443 887.207818990653657.P117 445 (5,89) 2671.1460384540571001412284141831845453026637206635511.P55 447 (3,149) P89 449 1256303.6871197486841.3578620616468306981503. .526385733768051189441947168504909159.P59 451 (11,41) 18041.216481.9718704501529.538939720215834697.P80 453 (3,151) 790468905817.P79 455 (5,7,13,35,65,91) 200201.P82 457 150327409.P130 459 (3,9,17,27,51,153) 407770693450231393.24418671951944649151.P50 461 2767.358228856441770927.7099353734763245383.P99 463 11113.3407681.448747600991881.239932071009857681156251129. .385606580062688087218266143.P62 465 (3,5,15,31,93,155) 2791.103231.P65 467 121606801.1148984537885906196977362003686090739460725564747973734847.P76 469 (7,67) 70321958644800017.1839633098314450447.P84 471 (3,157) P94 473 (11,43) 12853303.133139883512681.4193551379485561391. .1703616691469833244854254847.P60 475 (5,19,25,95) 4751.18020551.1369738735713888876695951. .113709467433878120743807151.P48 477 (3,9,53,159) 94447.4879711.242003089.P74 479 33385343.6293443049. .683481445118041278287416124073722711169070307627777892361.P71 481 (13,37) 138724733805016586033.5800976318060644948970424014255729.P76 483 (3,7,21,23,69,161) 967.18423553.172384633.1186694555374004016103.P41 485 (5,97) 10084875238121.34224064338126003049783351. .6424414731245950286450458211761.P46 487 4871.P143 489 (3,163) 836191.355307401.116539854237679.619079222361672204943.P48 491 983.7707719.110097436327057.6976447052525718623. .19970905118623195851890562673.3717542676439779473786876643915388439.P41 493 (17,29) 3616649.10353001.P121 495 (3,5,9,11,15,33,45,55,99,165) 991.334202934764737951438594746151.P40 497 (7,71) 6959.254461617383.P111 499 20959.1998447222711143545931606352264121.P113 501 (3,167) 25129004796912072003423103.P75 503 3213684984979279.12158987054135300783.1873030665061080894263.P96 505 (5,101) 1906785849099933631.P102 507 (3,13,39,169) P94 509 12619129.19089479845124902223.647125715643884876759057.P104 511 (7,73) 15212471. .144780974187086260903935034761413745643636578290924150417.P67 513 (3,9,19,27,57,171) 57457.35473416481.121323854647.2237717449946593.P56 515 (5,103) 1031.989831.960954217134424245898328814050043401.P78 517 (11,47) 82721.387348809.1292800939332382943. .270374114136830957955241.26302895729179572365768002599674239.P49 519 (3,173) 1039.P101 521 P157 523 160188778313202118610543685368878688932828701136501444932217468039063.P90 525 (3,5,7,15,21,25,35,75,105,175) 4201.7351.181165951.P57 527 (17,31) 13306086595097866632236752730067629415649399. .50061214622509969230528187280149191683596667776057.P52 529 (23) 54999142147740840245669969.347916608026315949237260151. .9114901722266383629807574332217258944092868367.P55 531 (3,9,59,177) 1063.288236359.196629322303.15888898944343. .8099559410464120708848563721343.P38 533 (13,41) 166297.744487658617.P128 535 (5,107) 12841.95231.879622391.331343920853356078376431. .23718232032401560617445166686464799001.P49 537 (3,179) 4297.16111.196543.P94 539 (7,11,49,77) 234341789260493933662402728271919.P95 541 4312790327.6115209994009.77146448294831869472151022106713. .904106555381898703253733254107256591.P73 543 (3,181) 1087.534955385319592511227419175872576025063351.P64 545 (5,109) 3271.213641.18109412991311.2511696210834096991. .7647513170903349335637401.P65 547 5471.172720604638150729.157552196128597543991.P124 549 (3,9,61,183) 38431.1386525709821079.P89 551 (19,29) 4409.14327.27551.P140 553 (7,79) 166153042787383.P127 555 (3,5,15,37,111,185) 27751.P83 557 3343.21993703.4565508951414453792719. .22053236096920219270632521586535711.P101 559 (13,43) 3180000071.9215285895065526291256518741915902569.P105 561 (3,11,17,33,51,187) 146983.2009643799642447.P77 563 2815747080256641401887817.13299213974872825932452460424235657.P111 565 (5,113) 185318160171793066961.29444549303703754611026537050435001.P80 567 (3,7,9,21,27,63,81,189) P98 569 15854617.55470673.182602768015690099110572536951. .110582329556343704552404016904356632250881.P87 571 5711.27409.69693366045316671685098712301007940958018325270028\ 49548226132675916172927.P91 573 (3,191) 32788207.P107 575 (5,23,25,115) 1151.13220653410551.P117 577 3463.132305774316967.P157 579 (3,193) P116 581 (7,83) 798037199.175908273685537. .15444711420006203351165170879848557117713.P85 583 (11,53) 755569.65780528969.106077807287.P129 585 (3,5,9,13,15,39,45,65,117,195) 2400314671.339175003117573351. .255375215316698521591.P40 587 554129.2926783.39483330766889.73208283304744901303. .3728298863422039632638351.P107 589 (19,31) 18083479.36064471. .2023706519999643990585239115064336980154410119.P103 591 (3,197) 407791.50070703.304292056417.P93 593 104369.3061144307110551703729. .4027016481761119763553952463965455549881.P113 595 (5,7,17,35,85,119) 34511.199921.69935987114957671.P90 597 (3,199) 5066143.1445406523039.P101 599 16659379034607403556537. .148296291984475077955727317447564721950969097.P114 601 3607.64863527. .643390760896826272806925563059612685509039265031067456849993.P110 603 (3,9,67,201) 648168721774409511378116151410898673195879.P78 605 (5,11,55,121) 3631.143448045841.P118 607 P183 609 (3,7,21,29,87,203) 15109165329245515231985834925494692879.P65 611 (13,47) 1223.1609655415875897360904371080437164611501156560743.P115 613 44599476833089207.332817722770314187794325446534549089.P133 615 (3,5,15,41,123,205) 1231.49201.92757531554705041. .3427007094604641668368081.P48 617 59233.68954123297. .157751978115225385495647532421006478127229405644601.P120 619 110183.710820995447. .109378681671075297195692480234213908123642560192251038455204252439.P105 621 (3,9,23,27,69,207) 624456487.93747988411543.P97 623 (7,89) 74383430474532481. .74716964067758844321661890925503011337830328521.P95 625 (5,25,125) 1277297679372570001.573759820507018639639785001. .18152902839291497575027462639977160832701118299213751.P54 627 (3,11,19,33,57,209) 11287.12471031.89856878697433. .8778523027466598416204656058467252273.P47 629 (17,37) 45470534643405479586527115047619453123209. .205296815265168567756164047567360097447247109142889252157111.P74 631 333628015107245479.474640860193534882628078580680807822523991.P131 633 (3,211) 2399291551.17689153588009.60560850681938908875991. .9970146666059203361408046051199.P50 635 (5,127) 5081. .83615338235826681881707602454578099792649940383635851698961.P89 637 (7,13,49,91) 3823.15289.31945881241.153925026222241.8573192048327176271. .6044274266901603399200353.153472677405951306470238401460959.P44 639 (3,9,71,213) 1279.84462210560148142953097. .1329628131546931497103420134367.28435302301212461494420074814087.P39 641 35897.49999.1173835097.2401258891949526685926151441. C148 643 3189281. C188 645 (3,5,15,43,129,215) 46441.4175568751.1728221461577944661374351. .83212524822005103181053031.P37 647 303303806129303896428103.11502383762931955619183430785983.P141 649 (11,59) 649001.23952086159.34418203155300430111979265857.P130 651 (3,7,21,31,93,217) 1303.1191622782866437328993110351.P79 653 78557207.289837969.16008527538753578495897. .3044938125828889184039273431.3786707123184812723340717607.P103 655 (5,131) 597361.2576754528566814601.351182936972570824983481. .15333541100090824437129533485272856744656791.P66 657 (3,9,73,219) 73*.10178663167.27265714183.5271393791658529. .2762194134676763431.42185927552983763147431373719.P45 659 1319.11527429277532648241.626564962613678012662146877852049.P144 661 1330270433.3370159489168519.1009157848082361225065617. .118420287267066844820208926433723871.P116 663 (3,13,17,39,51,221) 47737. .1817023253798585112376955621635919346759818823715057.P60 665 (5,7,19,35,95,133) 161517058694951.P117 667 (23,29) 12007.458897.88039999.246270735864387271375789289856617. .14508653262991734676225669411020750337.P98 669 (3,223) 182224921317852297530287.P111 671 (11,61) 116356769.33491655209.64110547427930873. C145 673 581163767.41283139633378645724930694480520226273492263. C151 675 (3,5,9,15,25,27,45,75,135,225) 1605151. .1094270085398478390395590841401.2842496263188647640089794561760551.P39 677 1943118631.531132717139346021081.978146583988637765536217. .53625112691923843508117942311516428173021903300344567.P98 679 (7,97) 6791.59753.93703. .1337351764099536062382592381405648316666025584913912478511.P103 681 (3,227) 962744903648208108713898832235090314894033.P94 683 1367. C203 685 (5,137) 119191.7084271.83648644144524510111773141111.P123 687 (3,229) 6871.2104809991.175932323679511304414371921.P98 689 (13,53) 135995976143.1067583682127. .1372617429248257063179636119999552844862152089.P120 691 906642603313.10488160032325844521.2833637724427940664433391497. .16636201944470267267182958207.P122 693 (3,7,9,11,21,33,63,77,99,231) 289511839.2868251407519807.P85 695 (5,139) 3452778071.3578189431.225797717267637708506527464987314161. .901584692755427378722839770656354167189649601351.P64 697 (17,41) 16729.P189 699 (3,233) 1401190779823.1917765426328344646895407. .23482447257772948338207752516264041.P69 701 796337.2983457.28812503.1073825104511.9983923992673. .15865578195367.40686928318417.P140 703 (19,37) 35284030283053759.1294046302848776287.11931812674076681849. .167823649475113693461122232089506777. .59588714597816906383348767955828416209.P69 705 (3,5,15,47,141,235) 157925605323676378629391.P88 707 (7,101) 126729751.128782811543.700553271665826444242790841. .3598194408030741269333601460682311. .51903872795463977962670556595700473584389435543.P54 709 216868921.1391646221255097953.P187 711 (3,9,79,237) 5689.41851365145831.864328108984548257763049805767. .19573690271784800408214873038427972853220421889.P48 713 (23,31) 68449.335203548019575991076297. C171 715 (5,11,13,55,65,143) 249602191565465311.598887853030285391.P110 717 (3,239) 40153.12417007.58392032593.55009358369431. .199987538790826996082414586220862745720625115339053303.P54 719 1439.772207. C208 721 (7,103) 10550281065119153.P168 723 (3,241) 1447.7480159.102072660983478595344638863.P109 725 (5,25,29,145) 448477751.245573800535260692993906074551. .177457540153273192963355393450351. .3306918468362395868346324514646813146301551.P56 727 C219 729 (3,9,27,81,243) 80191.97687.379081. .664728004346558283448724389870269691211809.P90 731 (17,43) 67872792749091946529. C183 733 694653525743.14399141148866077141941966959399761. .13948432601001273785699253868326270649.P138 735 (3,5,7,15,21,35,49,105,147,245) 41161.4163041.20147473081. .2340389488711.27653710336343911.P51 737 (11,67) 4423.12148690313.5157050159173695487.17904041241938148871927. .1963672214729590922916323781834466879.P108 739 184603056517613273120809.48050683584092004380805463790111. C168 741 (3,13,19,39,57,247) 83352127.2665675660861389884202429169.P95 743 1487.1219280833.14904366017.118722715461092305629361. .4721525455401597740684262559.C151 745 (5,149) P178 747 (3,9,83,249) 324965201690131831.P131 749 (7,107) 46439.120618551047.227444841245238451591. .963644196044828188869351734353847. .4143416085716681490838653625856664863812512904964849.P71 751 C227 753 (3,251) 4519.12049.220116640729.180797717027593.P117 755 (5,151) 1511.15073467791.286621334502631.P153 757 9815263.561595591. C213 759 (3,11,23,33,69,253) 1633369.46025761.P119 761 4567.6089.738686421813192728921171408273447. C189 763 (7,109) C195 765 (3,5,9,15,17,45,51,85,153,255) 16831.3696481.2109936092650831. .24710462787135943791475548268920478656481.P50 767 (13,59) 38351.297205245433279.6616963204951529.6329588309789019577199. .756450142211646020278834399577.714106625397559765944265428336645929.P87 769 1591805393.6123566623856435977170641.P198 771 (3,257) 1543.P151 773 6864241.9461521.1165626988664823792549971253972697. C186 775 (5,25,31,155) 3064351.2168815801.1113614148551.P153 777 (3,7,21,37,111,259) 4663.6433561.4750535347861726648681. .96786396648673403672115546439.P70 779 (19,41) 1559.3142487.21726311.104003232119.164597693569197241. .202664437974567925010435751833. .539043252861508730639718553683237826728217905315243065969.P86 781 (11,71) 6511616671913.66232837958133438967.79034734517219615663. C158 783 (3,9,27,29,87,261) 1567.602999957032279571271592229136193. .1345967414522954303164296915490846371433.P77 785 (5,157) 5393364481.135732250385154376731523201. .2167731870412324810536209829271. .14488318273595902692706536553684238317387680182551817911.P67 787 9951597611230279.96512008100928793. C204 789 (3,263) 5609685181351.274473195338134592222791.585608533119706764820561. .748093847626791888666559.20389292512407050043445124186439967.P40 791 (7,113) 1583.7920714887. C189 793 (13,61) 4759.31721.145211798447.579981948313. C186 795 (3,5,15,53,159,265) P126 797 2006858753.54573369937.104757762864135516671. .747609928190821086986322983.21023711323746974956423747989180911.C139 799 (17,47) 2957111053582540504996549489605401. C188 801 (3,9,89,267) 3344977.16960539007.1790799748670521. .138732415594618114488007.2326974010504075618187561564812777.P71 803 (11,73) 1607.78366377.1384018681.1533745237729. .2762339998302448893880313142073.P154 805 (5,7,23,35,115,161) 13816619111. C150 807 (3,269) 2771239.502502761.P146 809 C244 811 326023. C239 813 (3,271) 24391.2248759.36936217.152948738791.49322756803485314471713.P111 815 (5,163) C195 817 (19,43) 81278478804329.1527890378338261467896809. .503836749763922905688176944079261201.C154 819 (3,7,9,13,21,39,63,91,117,273) 2681001528674743. .219516331727145697249308031.P89 821 419273207.109840721427977.286121480219517473. C208 823 1460915248436556406607.1534086200463688788034864584049. C197 825 (3,5,11,15,25,33,55,75,165,275) 702948566745151.9115784422509601. .4108316654247271397904922852177568560929751.P48 827 66161.1637241673.1656489332706171370072190422631. .2550707823005230793212015514781257.C172 829 72953.89654239955972104838901500177.P216 831 (3,277) 1663.3772542223.502746492223.660284006953.679758314119.P118 833 (7,17,49,119) 14821647473599.2394594520709878135254356190088519028761. .794769178865803830796254438307018567389833. .16248173432447880508878672460681334430321473.P65 835 (5,167) 18144551.44596548025921.819048171793389082617855311.P152 837 (3,9,27,31,93,279) 1127316245518063.P148 839 26849.138561000316919.377801626929390823. .113910681722635191781067775764311.P185 841 (29) C245 843 (3,281) 1390916281.2475486361.P150 845 (5,13,65,169) 4493034001.53928095661079461754990292241379839311.P141 847 (7,11,77,121) 42262784685026262370553.P177 849 (3,283) 18679.147727.353712117583777.29940168528270618887118001.P121 851 (23,37) 1530328553290391228929969.11862938913865507127049391.P189 853 2065711807.513740645819473.4727997228805279065233. C212 855 (3,5,9,15,19,45,57,95,171,285) 709018264240844065111. .158362232618940822526398920291451047671.P72 857 6857. C255 859 7215601. C252 861 (3,7,21,41,123,287) 5167. .209530011998277670096922500900062393290897233.P97 863 8258911.169382737.175642891399. C234 865 (5,173) 526769431.P199 867 (3,17,51,289) 5266159.P158 869 (11,79) 361592639.239506881856626095535121.P203 871 (13,67) 15679.95860519.12708237958354187384010097. .791926693391795441127294795391450663. .137403482726882442386895575645854007713.P127 873 (3,9,97,291) 132697.9449353.7969524463.P152 875 (5,7,25,35,125,175) 725688486718330087751.P160 877 35081.1436527.1839699736969340949026772071177. C224 879 (3,293) 1759.288313.142891999.4010077111.12760970401. .4703954662078801.94031095460270951212691599.P98 881 26431.P261 883 8831.63577.258777491057348926546569104663.P228 885 (3,5,15,59,177,295) 2756788662198217256191.P119 887 16173559.139714099995626040378049.2382154297313396649423300881. C210 889 (7,127) 127*.P226 891 (3,9,11,27,33,81,99,297) 1783.12430037668834128259094186647.P132 893 (19,47) 6705767506519. C237 895 (5,179) 21481.6917353530526492681.78961972629651529859281. .380175443574763153088777745842279962515778711. .1696067654151459074824290253436397570222341162468471.P73 897 (3,13,23,39,69,299) P160 899 (29,31) 460289.110521633444549751. C230 901 (17,53) 114684958103.5033986097724889062887.P218 903 (3,7,21,43,129,301) 514711.P147 905 (5,181) 121271.1163487911. C203 907 1170031.3256645177.131895016205024767.P241 909 (3,9,101,303) P181 911 1823.26129303.201955048939840841121786425435009.P232 913 (11,83) 35913067887863. C233 915 (3,5,15,61,183,305) 360511.95805951836468022966692945378791. .8013930086014783164580302226587271.P74 917 (7,131) 5503.229268017217.57193908443040877545241. .161226249164751695652113.573472334735477809996357383167. .3150916688576664143611069445209929619169. .183441131803022762130427722962952171341869050463.P57 919 33554520197234177. C261 921 (3,307) 85724839.1240718764955671.7718960266212068280249289.P137 923 (13,71) 1847.5619297841. C240 925 (5,25,37,185) 27281951.86759605608601233853529454601.P181 927 (3,9,103,309) 46351.2033839.22229194879.312842300671. .1561132657829329085404515097.16549888083084083065824727273.P96 929 13007.340388595097. C265 931 (7,19,49,133) 14897.67033.4768748142197177447.P200 933 (3,311) 37321.13129750729.188999403857128746828420806061841. C140 935 (5,11,17,55,85,187) 1871.3706347481. C181 937 28111.2419437071. C269 939 (3,313) 1879.995114641.147859967407. C165 941 7529. C280 943 (23,41) 9431.39607.21698431.62209711.138325941036565103. .9280993516297855054039457.57644473457648767005697802783.P171 945 (3,5,7,9,15,21,27,35,45,63,105,135,189,315) 124339521078546949914304521499392241.P95 947 295130657.25749931927.4621646208862937. .11892980076500863942962129100776937.C217 949 (13,73) 22777.78341849.427960745238703.705900082312653909721. .377725045152842556276329.C189 951 (3,317) 241459659973825303567826493454039. .1378790948509427717673789094900757220589207. .1271824819271756089692072867669700519167079543.P71 953 343081.562070136841.40496650491842199555367. .824501439026637805612489876810823.C215 955 (5,191) 17191.91259801.1645375231.385888918596723595535405951.P181 957 (3,11,29,33,87,319) 1609806083534335902079374125310994612192903. .69586779567906400453376529267198885406422141822768937.P74 959 (7,137) 23017.531287.12959927.12966664479880063. C213 961 (31) 280651416271709745866686729. C254 963 (3,9,107,321) 14662639. C185 965 (5,193) 2184761.204948631.86710817849281.44894058474254631045721.P180 967 23209.549257.1438495818172960049. C263 969 (3,17,19,51,57,323) 11726744977.540538609159. .78161016568215708061327.432185728407904618000990086610965513529.P91 971 C293 973 (7,139) 2356070859382001284653313.2166176541500493808960173319. C198 975 (3,5,13,15,25,39,65,75,195,325) 1951.8837728285481551. .26155966684789722885001.1663763381192308635718252801.P76 977 867577.1813313.2069655374719577273.49858990580788843054012690078841.C232 979 (11,89) 89*.13815649.7883576248112389199.P237 981 (3,9,109,327) 10341703.499601719.9727892263.128014683020611040553769. .8290249522204489310786895351990721. .206372514331790653651181848993175421190047559657.P65 983 1808226257914551209964473260866417929207023.P254 985 (5,197) 70921.7263391.73518775918537446144887630711. C196 987 (3,7,21,47,141,329) 9585228595374769.512512927677384344303149537.P124 989 (23,43) 31649.36706221574691349767448834021945679. .1844138946953172296553312102102187271.P203 991 8218291649.41473350001.231620367206687. C264 993 (3,331) 23833.55609.857491387188810516016046647. .921777666286057213147728970951.P133 995 (5,199) 14369791.41735340671.114443156761. .2949578944598743237863911.32308603398271777835967540631.P157 997 C301 999 (3,9,27,37,111,333) 7993.473589937. .610750585993378533918571366551132613003293697.P138 1001 (7,11,13,77,91,143) 6007.6952744694636960851412179090394909207. C177 1003 (17,59) 605829388649921.1629239097907113911209. C244 1005 (3,5,15,67,201,335) 68626625145959029951. .663636889167401354279502795531186216903001.P98 1007 (19,53) 37430191.183802578728708044103. C254 1009 3454817.198582684439.20649907789079.21624641697047. .30850253615723594284324529.1134327302421596486779379019599.C204 1011 (3,337) 39147943.6853410184776097.P179 1013 6079.71486759597273. C288 1015 (5,7,29,35,145,203) 2154593281.P194 1017 (3,9,113,339) 54919.72386347544037768298632733630815274606848381343.P151 1019 2039.75407. C299 1021 40841.795808241.51731968308257. C281 1023 (3,11,31,33,93,341) 105586579766713. .91979404475310284038389763276277647.P132 1025 (5,25,41,205) 6151.2252951.2721217151.1330118582061732221401. .12477521332302115738661504201.519724488223771351357906674152638351.C137 1027 (13,79) 452599156086559.17560235101945245417825001. .67545455787839926022098207.C216 1029 (3,7,21,49,147,343) 7*.6896727944023.2714819157586383751. .3274162442129276091367. .5878920553871871291270984955318098156844648537.P78 1031 2063.435502649. C299 1033 196271.36913223.88910338973359434076776038119074340716281. C258 1035 (3,5,9,15,23,45,69,115,207,345) 19616702141919323129388715950912065791. .647463932206559821122945033207524451183068970139360141681.P65 1037 (17,61) C289 1039 5080711. C307 1041 (3,347) 24769991104728312891937.P186 1043 (7,149) 2087.100129.3256247.7346919119. C243 1045 (5,11,19,55,95,209) 6271. C214 1047 (3,349) 18063321433.P200 1049 33569.459463.1059099980653317121.P288 1051 3575503. C310 1053 (3,9,13,27,39,81,117,351) 44207047.24295813738965169951447.P166 1055 (5,211) 2111.29257554834707791. C233 1057 (7,151) 5318798633.117801297041.6645418768842321985721.P229 1059 (3,353) 18861552481. C202 1061 C320 1063 1485761479.P311 1065 (3,5,15,71,213,355) 14139262262808175798602566204793985440361. .6252200505559391265660834611730277041893919359311.P80 1067 (11,97) 4884727.32805679003831689475103. C260 1069 17481727674576239. C306 1071 (3,7,9,17,21,51,63,119,153,357) 10711.861229657.52877551231. .91005071977.5880734007124467829187484937. .2044333418084691639917563561172180103378559.P69 1073 (29,37) 44197213979727234355841. C281 1075 (5,25,43,215) 4718966201.P244 1077 (3,359) 247711.13759551679.P200 1079 (13,83) 417042099631.1104547173371974879.1234944495181377943. .112521450818457950210174975426777.C217 1081 (23,47) 47*.3137063.2756059353782849.1248432852603561685630837661279.C251 1083 (3,19,57,361) 14107651849. C196 1085 (5,7,31,35,155,217) 217001.553351.105254261561.319268480441.P184 1087 10722169.2144921195591.33990250708335239.2105485879475562449. .421733524843190780249388261839156579767.C235 1089 (3,9,11,33,99,121,363) 141641296831.27306046411338223. C172 1091 87281.551978359.791343585595817.97535130364653673535422113471207017.C265 1093 43721.111487.42565880168703357316051447. C294 1095 (3,5,15,73,219,365) 702595801. C165 1097 980719.4666639.22926719175799.1734492765338661710171833. .36079584237927411511333522577.205295973898620029528272537868263.P220 1099 (7,157) 11302318217.28617130498420804403756708531447.P240 1101 (3,367) 79273.258977744356523549983.883533090360873723903538281367.P165 1103 2207.4126110275598714647074087.P305 1105 (5,13,17,65,85,221) 7555991.115812024214750631. C208 1107 (3,9,27,41,123,369) 7675195491326802969559.472897006006202784083089.P172 1109 30963501968569.85608965982066833903. C301 1111 (11,101) 457892136759270759480793. C278 1113 (3,7,21,53,159,371) 15583.51199.2363026390394916673046830675466863.P146 1115 (5,223) C268 1117 53617. C332 1119 (3,373) 2239.20143.154565233.1100558881.P199 1121 (19,59) 8969.P311 1123 777288435261989969. C321 1125 (3,5,9,15,25,45,75,125,225,375) 213751.150212580033138336342001. C153 1127 (7,23,49,161) C279 1129 33871.833798113. C327 1131 (3,13,29,39,87,377) C203 1133 (11,103) 29237863091999.49785726347323441303511. .2468805350190760992979935216750635087.C235 1135 (5,227) 132839238602148428191.4503031418785283725652516551. C225 1137 (3,379) 3289098531153894127. C209 1139 (17,67) 138959. C313 1141 (7,163) 301230847.16742221609.14493503199673.628007894034529. .131380422697420095809.875938090182754292028329. .106014123028829664722111227465753.P170 1143 (3,9,127,381) 518814559.100342091647341370469161844713.P190 1145 (5,229) 4946401.199439000998738772588908077106387241. C233 1147 (31,37) 100937.9245269025364933413947751633. .141807120921029844210677840999.C263 1149 (3,383) 2651552381122661167.12917254515820483569633735619111. C181 1151 284278475807.81344898763887260484533897.658622107254745112979229913.C283 1153 267497.84755607199. C331 1155 (3,5,7,11,15,21,33,35,55,77,105,165,231,385) 2311.6250631311. .494224324441.P120 1157 (13,89) 1675125010930879.5519267814834477438497153. .8835538898098695059049137.15472078121378442801745561.C228 1159 (19,61) 185441.56256385753. C309 1161 (3,9,27,43,129,387) 6967.5979151.60499150497847. C204 1163 848181715001.337097300570078978047. C318 1165 (5,233) C280 1167 (3,389) 60459128773735346116971161647. C205 1169 (7,167) 514361.6020351.7322617.8932786385279.P268 1171 153606920351. C342 1173 (3,17,23,51,69,391) 428417137.18228580446571609.403906782348344599. .515878737178649880676177.C146 1175 (5,25,47,235) 10009431316533167951.1094883804311836270751. C237 1177 (11,107) 3775817.5960329. C306 1179 (3,9,131,393) 28297. C231 1181 4742897.196834168670106625096599487. .199668911054466914791190422986407.C291 1183 (7,13,91,169) 28393.46655969015605951. C261 1185 (3,5,15,79,237,395) 115150116391.21792652855138681.P161 1187 256393.113603023.1761533117965696212626325049982897. C311 1189 (29,41) 600619547820455607135590639621491727. C302 1191 (3,397) 274404635931475033688839.10712613085162141902489577. C190 1193 121687. C355 1195 (5,239) 270071.10602041.150885481.502862692004168161. .4925687525543853241.C230 1197 (3,7,9,19,21,57,63,133,171,399) C196 1199 (11,109) 2399.174181129. C314 Table 2+(odd) Factorizations of 2^n+1, n odd, n<1200 n Prime Factors 1 3 3 (1) 3* 5 (1) 11 7 (1) 43 9 (1,3) 3*.19 11 (1) 683 13 (1) 2731 15 (1,3,5) 331 17 (1) 43691 19 (1) 174763 21 (1,3,7) 5419 23 (1) 2796203 25 (1,5) 251.4051 27 (1,3,9) 3*.87211 29 (1) 59.3033169 31 (1) 715827883 33 (1,3,11) 67.20857 35 (1,5,7) 281.86171 37 (1) 1777.25781083 39 (1,3,13) 22366891 41 (1) 83.8831418697 43 (1) 2932031007403 45 (1,3,5,9,15) 18837001 47 (1) 283.165768537521 49 (1,7) 4363953127297 51 (1,3,17) 307.2857.6529 53 (1) 107.28059810762433 55 (1,5,11) 11*.2971.48912491 57 (1,3,19) 571.160465489 59 (1) 2833.37171.1824726041 61 (1) 768614336404564651 63 (1,3,7,9,21) 77158673929 65 (1,5,13) 131.409891.7623851 67 (1) 7327657.6713103182899 69 (1,3,23) 139.168749965921 71 (1) 56409643.13952598148481 73 (1) 1753.1795918038741070627 75 (1,3,5,15,25) 1133836730401 77 (1,7,11) 617.78233.35532364099 79 (1) 201487636602438195784363 81 (1,3,9,27) 3*.163.135433.272010961 83 (1) 499.1163.2657.155377.13455809771 85 (1,5,17) 26831423036065352611 87 (1,3,29) 96076791871613611 89 (1) 179.62020897.18584774046020617 91 (1,7,13) 224771.1210483.25829691707 93 (1,3,31) 529510939.2903110321 95 (1,5,19) 2281.3011347479614249131 97 (1) 971.1553.31817.1100876018364883721 99 (1,3,9,11,33) 5347.242099935645987 101 (1) 845100400152152934331135470251 103 (1) 415141630193.8142767081771726171 105 (1,3,5,7,15,21,35) 211.664441.1564921 107 (1) 643.84115747449047881488635567801 109 (1) 104124649.2077756847362348863128179 111 (1,3,37) 3331.17539.107775231312019 113 (1) 227.48817.636190001.491003369344660409 115 (1,5,23) 691.1884103651.345767385170491 117 (1,3,9,13,39) 5302306226370307681801 119 (1,7,17) 823679683.143162553165560959297 121 (1,11) 117371.11054184582797800455736061107 123 (1,3,41) 739.165313.13194317913029593 125 (1,5,25) 229668251.5519485418336288303251 127 (1) 56713727820156410577229101238628035243 129 (1,3,43) 1033.1591582393.15686603697451 131 (1) 1049.4744297.182331128681207781784391813611 133 (1,7,19) 4523.106788290443848295284382097033 135 (1,3,5,9,15,27,45) 811.15121.385838642647891 137 (1) 1097.15619.32127963626435681.105498212027592977 139 (1) 4506937.51542639524661795300074174250365699 141 (1,3,47) 1681003.35273039401.111349165273 143 (1,11,13) 2003.6156182033.10425285443.15500487753323 145 (1,5,29) 7553921.999802854724715300883845411 147 (1,3,7,21,49) 748819.26032885845392093851 149 (1) 1193.650833.38369587.7984559573504259856359124657 151 (1) 18717738334417.50834050824100779677306460621499 153 (1,3,9,17,51) 123931.26159806891.27439122228481 155 (1,5,31) 11161.5947603221397891.29126056043168521 157 (1) 15073.2350291.17751783757817897.96833299198971305921 159 (1,3,53) 6043.4475130366518102084427698737 161 (1,7,23) 8103467492759792327149800361564410265219 163 (1) 11281292593.1023398150341859.337570547050390415041769 165 (1,3,5,11,15,33,55) 415365721.2252127523412251 167 (1) 62357403192785191176690552862561408838653121833643 169 (1,13) 4929910764223610387.18526238646011086732742614043 171 (1,3,9,19,57) 19*.19177458387940268116349766612211 173 (1) 347.4153.35374479827.47635010587.1643464247728189221623609 175 (1,5,7,25,35) 1051.110251.347833278451.34010032331525251 177 (1,3,59) 13099.4453762543897.1898685496465999273 179 (1) 58745093521.4347868190665879373495950562775707707143803 181 (1) 1811.31675363.17810163630112624579342811733978085990447907 183 (1,3,61) 1772303994379887829769795077302561451 185 (1,5,37) 1481.28136651.778429365397887608540618330873281 187 (1,11,17) 2191165825376888084750157716424579062015865776131 189 (1,3,7,9,21,27,63) 379.119827.127391413339.56202143607667 191 (1) 1046183622564446793972631570534611069350392574077339085483 193 (1) 6563.35679139.1871670769.7455099975844049.1280761337388845898643 195 (1,3,5,13,15,39,65) 107251.571403921126076957182161 197 (1) 197002597249.1348959352853811313.251951573867253012259144010843 199 (1) 267823007376498379256993682056860433753700498963798805883563 201 (1,3,67) 2011.9649.6324667.59151549118532676874448563 203 (1,7,29) 596834617.3692022713.252715814615565962418688965855731 205 (1,5,41) 2125820563389437533390243893834597846757304863651 207 (1,3,9,23,69) 6113142872404227834840443898241613032969 209 (1,11,19) 419.3410623284654639440707.1607792018780394024095514317003 211 (1) 4643.9878177.5344743097.199061567251.22481127512575175864234185190299 213 (1,3,71) 5113.17467.102241.203525545766301306933226271929 215 (1,5,43) 9084611.59904608378705661377430182608711698924130721 217 (1,7,31) 16233337.140508608590164280225934233098866842745808905947 219 (1,3,73) 9070197542196643.3278244690156222434135906137 221 (1,13,17) 443.4714692062809.4507513575406446515845401458366741487526913 223 (1) 219256122131.20493495920905043950407650450918171260318303154708405513 225 (1,3,5,9,15,25,45,75) 4714696801.281941472953710177758647201 227 (1) 297371.3454631579714210387.P44 229 (1) 18754643.P62 231 (1,3,7,11,21,33,77) 14323.P32 233 (1) 467.27961.P63 235 (1,5,47) 328006342451.461797907949997211.P27 237 (1,3,79) 647011.13664473.P35 239 (1) 340337.32605142983704221670173899.P41 241 (1) 2411.10411181203.15059828108442641.P43 243 (1,3,9,27,81) 3*.1459.139483.10429407431911334611.918125051602568899753 245 (1,5,7,35,49) 491.15162868758218274451.P29 247 (1,13,19) 207481.10049443.355011619.P45 249 (1,3,83) 9202419446683.P37 251 (1) 238451.P70 253 (1,11,23) 4049.85009.31797547.81776791273.P40 255 (1,3,5,15,17,51,85) 12241.418562986357561.51366149455494753931 257 (1) 37239639534523.518144156602508243009.P43 259 (1,7,37) 1456235596904319041738812533139.P36 261 (1,3,9,29,87) 523.6929826139.3453412901832690553.33563856450515702761 263 (1) 1579.92051.29261114397558193.P55 265 (1,5,53) 593783678966863030035641.P40 267 (1,3,89) 3739.4273.P46 269 (1) 424255915796187428893811.P57 271 (1) 1627.115417966565804897.4635260015873357770993.P40 273 (1,3,7,13,21,39,91) 547.105310750819.P30 275 (1,5,11,25,55) P61 277 (1) 25792643401363.P70 279 (1,3,9,31,93) 26227.119232435043.85384915399027.6444365376140611199022187 281 (1) 563.5203536083.P72 283 (1) 1699.62827.2486265371.67535788803713.P54 285 (1,3,5,15,19,57,95) 1101811.P38 287 (1,7,41) 1723.84413238703660609.4336790831080504259.P34 289 (1,17) 72251.79187.1077971.18360250452977.197766803208315851.P36 291 (1,3,97) 25609.5636963037465601.581546606903256979.99695503427255026561 293 (1) 587.26371.33403.13453890779540632945331892129844577.P42 295 (1,5,59) P71 297 (1,3,9,11,27,33,99) 23761.694387.6215074747201.P32 299 (1,13,23) 2393.834490119087067.P62 301 (1,7,43) 43*.P75 303 (1,3,101) 112102729.P53 305 (1,5,61) 331841.31347559232075126851.P48 307 (1) 1249678499.4315199443523.210708825063558235331.P50 309 (1,3,103) 619.2473.15451.89620507.2400744384937.98277023988499. .68545852036177507 311 (1) 64067.P89 313 (1) P94 315 (1,3,5,7,9,15,21,35,45,63,105) 1765891.P38 317 (1) 326330579.491981122308467411.P69 319 (1,11,29) 121333341977.169523514238420211.25925516494438382632167017.P31 321 (1,3,107) 154723.20636399209.480625710015394052365153.P25 323 (1,17,19) 17795830908608814443.3211586054639813621611. .6319957642033539607139.2065255878519475622261353 325 (1,5,13,25,65) 3251.5840251.7812610577851.9860942209386451.P34 327 (1,3,109) 666427.6927735019.P50 329 (1,7,47) 659.762394321774681.P66 331 (1) 5297.2983001129.7520796641.8530674250842274717434530683.P49 333 (1,3,9,37,111) 304363.9853387597819.31031320083857011.P31 335 (1,5,67) 93131.P75 337 (1) 21569.5333388961.964094242760707.P72 339 (1,3,113) 156619.28448881.P55 341 (1,11,31) 647219.1434929.37368615235403.P65 343 (1,7,49) 2513690593.2883580030222424891.P61 345 (1,3,5,15,23,69,115) P53 347 (1) P104 349 (1) 131282633.P97 351 (1,3,9,13,27,39,117) 4247713303224552237738169.P41 353 (1) 3803909572078746837295094051706948091.P70 355 (1,5,71) 15524635883992211.P69 357 (1,3,7,17,21,51,119) 428401.P53 359 (1) 3536450843.1110671633637523.194193974563158088483.P63 361 (1,19) 6874301617534827509350575768454356245025403.P61 363 (1,3,11,33,121) 2179.19488182484739.P50 365 (1,5,73) 581874971.498386055746534779273231850742131.P46 367 (1) 2203.19819.146264881313513.20837062885084633147. .460233616861852066165180033789571.P37 369 (1,3,9,41,123) 18451.174907.26309368807003.P50 371 (1,7,53) 18351945672220987.10471846336802440580575859. .90338901802490793533882683.P27 373 (1) 60427.694579497316894264425661243659806371972188318857.P60 375 (1,3,5,15,25,75,125) 2251.19963778429046466946251.P35 377 (1,13,29) 13454377.P95 379 (1) 15012732261073.728040923721821697586308784409.P71 381 (1,3,127) 3049.38257184231365987.P56 383 (1) 1351710731785981752792617.5609122817914313723820539.P66 385 (1,5,7,11,35,55,77) 219980531.4362989211422861340320935785851.P34 387 (1,3,9,43,129) 109053678968940302364939183451.P47 389 (1) 1074456464321.1369379108017267.2742094407638203.P75 391 (1,17,23) 2347.1578859.194902553.291438334156037699. .29111948248642861801.P52 393 (1,3,131) 787.7237497065445543055003057643920459.P42 395 (1,5,79) 5531.1415681.P85 397 (1) 13499.321571.476401.17414009.P97 399 (1,3,7,19,21,57,133) 63841.11355690325205671380495907537.P33 401 (1) 18885983617.3178641606717935496778334833. .24789994689980013078275217373572023257787.P43 403 (1,13,31) 6449.18539.576759899.153633897920257.P78 405 (1,3,5,9,15,27,45,81,135) 6481.9721.74967931.2437880491. .448217524891.10360573664851.1969543281137041 407 (1,11,37) 15467.2248206137.25330067076999169. .42897689055449636582684640379732099.P44 409 (1) 176596029450915408652219208387. .18791937710720575305760721588966789412396307.P51 411 (1,3,137) 7663507.2017223347.2707079449.P57 413 (1,7,59) 827.170735974773267443.P85 415 (1,5,83) 116201.134396921.P86 417 (1,3,139) 441187.1694689.392856131525846647191238066992041449.P36 419 (1) 5867.548560489336890960473978059.P96 421 (1) 4211.32983076027612611.P107 423 (1,3,9,47,141) 85693033.6596828416459.P63 425 (1,5,17,25,85) 91362251.5046718903451.P76 427 (1,7,61) 57461778571.1340235308854811506044205739394787.P65 429 (1,3,11,13,33,39,143) 859.8340357737139637289786276330761.P39 431 (1) 1807447391779.37452571239931.P104 433 (1) 2837017.P124 435 (1,3,5,15,29,87,145) 7060051.23476081.24578371.P46 437 (1,19,23) 7867.668214452631436913.315929758125865060721. .1905976815426273605733466333451.P47 439 (1) 3740281.5612260289.78527789689. .6563213024281378912864020513717469284499.P65 441 (1,3,7,9,21,49,63,147) 883.3529.22051.311347. .1996187656530838599012839257.P33 443 (1) 48731.489333371.2036829768181123. .203369567047358792597230853956871186267775970073.P57 445 (1,5,89) 7121.131865932411.40853155149612675915761.P69 447 (1,3,149) 19687929049.P79 449 (1) 194867.4332851.179293953141823358107657.P100 451 (1,11,41) 20747.21737299.2168435713049.P97 453 (1,3,151) 907.70089067.5667228215161742851.1302216832385373385027.P40 455 (1,5,7,13,35,65,91) 131041.1185685411.39537592800161.171525190684121.P45 457 (1) 6885357560205319573060633896800918448254904729193.P89 459 (1,3,9,17,27,51,153) 3673.98227.33204917536003441.572404735191016891.P44 461 (1) 99577.110641.4776428166707.108902775905377. .1017228587161022218598932642491638987.P66 463 (1) 2356759188941953.76834966209858049526107. .88119307925269041107418404833666787.P66 465 (1,3,5,15,31,93,155) 26041.316201.364831561.P54 467 (1) 33702457.48919673417.9516375589637513.133116327626495251. .759355003952701949854003.27312390961824038384529619828691.P34 469 (1,7,67) 408335956841.362312427317443674457. .76207764956885795275897986139.P59 471 (1,3,157) 290137.31255173993464476009.117791760059111382841. .207080154684218888000497.P26 473 (1,11,43) 947.8116681.4304613491867393. .2319326790833455848494271717419.P71 475 (1,5,19,25,95) 3145393391123750039342489201. .23352531315412606928823082635851.P50 477 (1,3,9,53,159) P94 479 (1) 3833.38321.7241702191810014332930493433. .54657255048286677488033160851148008819.P70 481 (1,13,37) 1484463163.116082946165734700021832375583736205537.P83 483 (1,3,7,21,23,69,161) 245641050541016665188014626987.P50 485 (1,5,97) 11238344415062964442147243324272630868644399851.P70 487 (1) 227020551154913939039124941009.P117 489 (1,3,163) 2840113.P92 491 (1) 15395951896033322050978817. .3563269486977651154759062020950904488457.P83 493 (1,17,29) 4931.244529.408071156372794293927147176542113833.P91 495 (1,3,5,9,11,15,33,45,55,99,165) P73 497 (1,7,71) 145915152433.5213526568247671787. .8705752060803157813200086999866476019.P60 499 (1) 163673.825347.61176403.1192425792950157874662150001. .1575585587524885013687391114684244158499565933913187.P53 501 (1,3,167) 304609.223318747.1134974373913.P75 503 (1) 2049744746263568646584566175908385907415012329005298331.P97 505 (1,5,101) 8081.223211.6909226326451.46393668925691. .145130814068214641.1025698740064276331.727679956595455269121.P29 507 (1,3,13,39,169) 10030854869257.4966300248405749059.P63 509 (1) 1019.1171175995519938934637486085538049.P117 511 (1,7,73) 3191707.10435643.44523886942460772001. .22310863847225018142861783673497419.P63 513 (1,3,9,19,27,57,171) 144667.1465129.P87 515 (1,5,103) 48111154791914771769582354405627641. .1925631536827398342750945451754630611.P53 517 (1,11,47) 220243.80765938529.635152101298808699. .41941878936097554082013916913.1398877133990750181532404877513.P46 519 (1,3,173) 7348400530773377989289144129092395161857.P64 521 (1) 501203.443418473521.90268296000189649868678102552775904610963.P99 523 (1) 36667531.83207209.129175771.11694270587.58052548129. .62802266052329939.P96 525 (1,3,5,7,15,21,25,35,75,105,175) 3205651.247772800801. .7223591273619001.129266711542799251.2310141222312973778401 527 (1,17,31) 3163.4217.578189648968825099.P120 529 (1,23) 17987.6190092443.8633301049969.P126 531 (1,3,9,59,177) 47065603823663026660218883.P80 533 (1,13,41) 354979.111719734852571.P126 535 (1,5,107) 205441.10155021917057853331411. .431458267304950409618673634079545142558161.P59 537 (1,3,179) 13963.54408841.170018474935706970530240356699.P67 539 (1,7,11,49,77) 12460603.31100269092898119731.P100 541 (1) 86561.59199467.396588707.512917469041.301118908380643. .84163674336698854450433.901912542742250747662095103224539896393.P54 543 (1,3,181) 3259.P105 545 (1,5,109) 1091.861926610031728629577011.P104 547 (1) 1533926272849.11514895455487400649824422273.P124 549 (1,3,9,61,183) 2146261699.37291324871089.165963031279777.P72 551 (1,19,29) 304153.400280563.P138 553 (1,7,79) P142 555 (1,3,5,15,37,111,185) 16975554121.22933014202051.38914392714281976571.P44 557 (1) 4457.124769.P159 559 (1,13,43) 326667346721.12553986510209.101119526079159121. .16404229182321439707977.33715476283025803700130451. .637467768535882654780280209.P36 561 (1,3,11,17,33,51,187) 1123.314161.153356423089. .2056186475270066900583885539731.P47 563 (1) 522114085011580241.74906924194076922022321.P129 565 (1,5,113) 19211.P131 567 (1,3,7,9,21,27,63,81,189) 562873504411.4744655685883.P74 569 (1) 10243.223439473.2058017388830521. .820793700834095033598534000634605722059739038841.P96 571 (1) 9137.73205584889.9640632099001.90794862316027093768853899468313.P112 573 (1,3,191) 8437952161.1063307289553.390527897582929297. .29489362305514321744929966859.P47 575 (1,5,23,25,115) 21851.270332801.1567238401.2299609001. .14807776819440781028664663654371485765148925580001.P52 577 (1) 75011.2796392419.19564699409833266851.P140 579 (1,3,193) 60217.92641.1036411.3497161.769643857. .313705683072406514521.187030532513381403767944747.P38 581 (1,7,83) 18593.219619.52588634980729.P125 583 (1,11,53) 17491.339307.2611841.492915077885080895226946001921.P111 585 (1,3,5,9,13,15,39,45,65,117,195) 1171.65521.26959262851. .43725552532343303477113703251.P40 587 (1) 2769467.13119770765051463547.58304599029582814346174509784\ 805811323612591021863318902938306546239131.P80 589 (1,19,31) 95419.59512561.208431792655914668791053468894512489769379.P109 591 (1,3,197) 8588408897489780521.2054021544734875175323. .171742076613580668857212300403179.P46 593 (1) 1187.62438341552073.6975729612775483517844546731.P134 595 (1,5,7,17,35,85,119) 2087022330866411.692218280897365325531. .165609143561652962744166091.P54 597 (1,3,199) 5153543358319177. .1616721141393989482351447740066663923511303121.P59 599 (1) 366994123.P172 601 (1) 9293424294571360217.P162 603 (1,3,9,67,201) 1460467.533471689.4484273898055819958731.P83 605 (1,5,11,55,121) 11*.715726621375769988310557612811.P102 607 (1) 115331.202769117249.16780869326776069043. .1622949422129340362249.1956783675173062584155810896697.P96 609 (1,3,7,21,29,87,203) 1602776802691.175314482313096251408712577. .17396456098240082242545082771.P35 611 (1,13,47) 821546524439369.36753316833775394448156716611. .38954799470098707550322754822902552371643630493051193.P71 613 (1) 628825424396562847763602356101542430347123271238646163429\ 2714267317577.P115 615 (1,3,5,15,41,123,205) P97 617 (1) 4937.2549322536147. .27507403322030377199658665104409171465823376047109547.P117 619 (1) C186 621 (1,3,9,23,27,69,207) 31051.25069771.1159185064537.5521094269128307. .185541553091188485307.55128155016097727617011127633.P31 623 (1,7,89) 59809.333929.390863971.P141 625 (1,5,25,125) 619324035675566251.232983411264923603130001. .983262166270913562877993411320001.P77 627 (1,3,11,19,33,57,209) 52711923798002218687534164008761. .97816902852991765949068317084025791019.P39 629 (1,17,37) 1259.2998322233.31438035163.1614575158577.335199740796521.P124 631 (1) 8309009.2530111867.4882057097.83188534509828089497. C144 633 (1,3,211) 3126092185651464401289035764906947922212259.P85 635 (1,5,127) 85091.431801.141512291.P134 637 (1,7,13,49,91) 225499. .4865853589671044882475767995199294334748858748304194627.P92 639 (1,3,9,71,213) 69779014917427.8970948423964301024591994817.P85 641 (1) 1283.32051.139739.353833.1078163. C169 643 (1) 1081756861144651.P179 645 (1,3,5,15,43,129,215) 1291.P98 647 (1) 4570409.9021769.932184694939. C169 649 (1,11,59) 72689.5804125093339.851030708304492139579. .248958833227314618649866043. .2025620548964486290862395942912830055105112948209849.P59 651 (1,3,7,21,31,93,217) 3926243469330528571.P90 653 (1) 1307.12550478467.739629398215461986863452049897. C154 655 (1,5,131) 104801.4235167121.52900187100851753648745461411. .17208429584639695721394569191520766721.P77 657 (1,3,9,73,219) 6571.17543368071267913387. .229746997821806461949873523193.P78 659 (1) 67219.284689. C188 661 (1) 206233.4611137.14330525250739.36640709883877569115302731. C148 663 (1,3,13,17,39,51,221) 8401537.1001115859537.61231726987393. .1139440451841756774164983271590070953.P47 665 (1,5,7,19,35,95,133) 7482637214297894380845818269728205334531.P91 667 (1,23,29) 2784059.25276633.77954721883. C161 669 (1,3,223) 247531.4340301546362831119363.P107 671 (1,11,61) 4027.48313.150238243. C165 673 (1) 1330725593.4061132942857.P181 675 (1,3,5,9,15,25,27,45,75,135,225) 377204851.578348287651. .126274316116265155801.635558882028912657106651.P45 677 (1) 2920579.6190489.4643444189241244139. .569759973030889624117974624560195467. .222155488792293038816414342324245378243.P98 679 (1,7,97) 48372050082931.486136475589650253586227318540449. .209263101129304381417185794914874527112788657.P83 681 (1,3,227) 4419691.4010501617. .2108728466430066008721288692506415323467900073343968942243.P63 683 (1) 1676083.26955961001.P189 685 (1,5,137) 920641.472748641.226338814638851. .236564778812552300459414801. .13166248872913462314441528794261286918041120435881.P60 687 (1,3,229) 779704994617.168813603058115744761. .81514868646704507393379787.P80 689 (1,13,53) 175083169.16181916011. C170 691 (1) 4668478921.9633758284523287289.5456646931831786367242204139. .53568019129739502623243476233360296971.P114 693 (1,3,7,9,11,21,33,63,77,99,231) P109 695 (1,5,139) 323414081.2444719759493201. .55048545633636680923804388123967583928006647872401.P93 697 (1,17,41) 107339.246739.234292369. C175 699 (1,3,233) 9551137.373746913.53590752072775417.P108 701 (1) P211 703 (1,19,37) 151849.9621259.9137976433.P174 705 (1,3,5,15,47,141,235) 29611.2708611.3059396467891.6830705352239611. .421803155659906892289931.667295426465706396181651.P24 707 (1,7,101) 1463491.16729032587.P165 709 (1) 340321.5045586197318561. C192 711 (1,3,9,79,237) 711001.377460666468258956042387138512734907. .2784647313277751541285980573724799363.P64 713 (1,23,31) 1427.1993292747.22816032820817. .1012570175762265527687179491024662141651.P135 715 (1,5,11,13,55,65,143) 519091.176510711521.166850044395914881. .6918033884710380409642384916290854761.P74 717 (1,3,239) 542487937.4633076102837130131059. .21719294766013521423128159168260255839743617.P70 719 (1) 34513.3138112889.4900402101963269918180361130213343099. C166 721 (1,7,103) 8248287587. C175 723 (1,3,241) 4339.153500131.5957570611.13423215628953313. .985424889624923045657501064259.P77 725 (1,5,25,29,145) 1451.372933190718801.49461103762004289880601. .1161722671658351672809136367089201. .1576422053186621557751857821413401.P62 727 (1) 11633.52068472442119144511578580563. .59803996769241650545074361210286131.P151 729 (1,3,9,27,81,243) 3*.227862073.3110690934667. .216892513252489863991753.1102099161075964924744009.P78 731 (1,17,43) 15316934231051174801. .15797542906128411931089923981198031035849.P144 733 (1) 396485324677401403.6032100214690846655623731769. C175 735 (1,3,5,7,15,21,35,49,105,147,245) 5881.P98 737 (1,11,67) 3556355492892313. C184 739 (1) 33407751111787921302306812882603339179.P185 741 (1,3,13,19,39,57,247) 1483.19267.P123 743 (1) 22291.4343579.6562222067.P203 745 (1,5,149) 2639421761.2113854074762921.8022560553172024220348389258622531. .51383124543331398511394411970333527291.P83 747 (1,3,9,83,249) 354854881.30495765703115017. .29004089048751837082775014755957683255977.P83 749 (1,7,107) 1499. C189 751 (1) 274867. C221 753 (1,3,251) 1307209.10212446539.95741909371.P124 755 (1,5,151) 54361.28992001.33673001.204764382884291.P147 757 (1) 417817067.P219 759 (1,3,11,23,33,69,253) 10627.4036363.44261191624217967508561. .83730859983591586460452561.P74 761 (1) 1523.1485778288798957523.32888267877547582651. .59133619649645058522941873.C162 763 (1,7,109) 17958105295747.747090793047295291603.P162 765 (1,3,5,9,15,17,45,51,85,153,255) 1531.6121. .33141833204828142196706150379164851.P75 767 (1,13,59) 10739.42953.1103294219. .66213049032039895442657530073798459769131.P152 769 (1) 36913.77836643.86369467.9401836358059.602141772875227166401.P177 771 (1,3,257) 831139.158530119801167697937. .10414600656781734361640396674583500992745231074293966400432773827.P65 773 (1) 533371.232063162200783964043837771355342619283. .1737639742639254060437861521344464381695829802369522859.232063\ 16220078396404383777135534261928387046186611079662143434527093563.P102 775 (1,5,25,31,155) 4651.282519050251. C166 777 (1,3,7,21,37,111,259) P130 779 (1,19,41) 384827. C212 781 (1,11,71) P211 783 (1,3,9,27,29,87,261) 12745935523. .44367700674110561467213850972770293767462491307345678065875601.P80 785 (1,5,157) 1571.25121.6412853401.P171 787 (1) 942827.5405369360996178738798259049. .44773841130192799148039136997839721.C169 789 (1,3,263) 255944062723386721566481.P135 791 (1,7,113) 54112378027. C192 793 (1,13,61) 50753.2864285210191809465583254126794859170149406203.P167 795 (1,3,5,15,53,159,265) 8088331.381199321.107814999632867521. .746485083287310097651.P72 797 (1) 875107.105670649433473243107529297593. C205 799 (1,17,47) 119851.16993492187603.81778526159866851701654313293617. C172 801 (1,3,9,89,267) 264331.3441291221723107683457. .36045123652756854086648245551969409.P98 803 (1,11,73) 11243.214863145125509028597735617.P187 805 (1,5,7,23,35,115,161) 33035981768945891. C143 807 (1,3,269) 11299.369345192417701052571. .18630342702315826557199328264881.466047024627224480211076768171369.P73 809 (1) 1619.14563.19417.601897.39595205804249.P213 811 (1) 7102927740195899.762653049249738822648895115723. C198 813 (1,3,271) 450403.88760231089.897186516077633497. .11170585420277403973061107961387073788895978930714757404139.P71 815 (1,5,163) 6521.11411.148331.P183 817 (1,19,43) 15840460057.P218 819 (1,3,7,9,13,21,39,63,91,117,273) 11467.13503673.P119 821 (1) 6569.1037866321911576169081957409.P216 823 (1) 316033.13615553872073. C229 825 (1,3,5,11,15,25,33,55,75,165,275) 10006979401. .65966684197384718027476767451.P82 827 (1) C249 829 (1) 131147801.3154069493397876555121. .2751096190869286949881816932924433.C187 831 (1,3,277) 9710343080872158664398414924796646767744190877182055\ 80112757800346489383481.P92 833 (1,7,17,49,119) 1667. C200 835 (1,5,167) P201 837 (1,3,9,27,31,93,279) 258451922773648099179883.P140 839 (1) 1377062372371126895706481139.P225 841 (1,29) 114377.2492918387059.26042075463217140565804312036553.P196 843 (1,3,281) 28383811.7317767583121. .1165121220595973490028272789835616165757454893337.P101 845 (1,5,13,65,169) 6761.103091.108161.367082334680413807808582241279931.C142 847 (1,7,11,77,121) 59359043484951383441635753. C173 849 (1,3,283) 6793. .125247878746743543692481610705995992666697711316774071921529.P107 851 (1,23,37) 542939.12985283780501700403. C214 853 (1) 2465171.7155452470451.14343826193517763. C221 855 (1,3,5,9,15,19,45,57,95,171,285) 6841.198098371. .23241389572585939528171.1175622349673189452424511749302390882321.P57 857 (1) 252182368360125289180898199073630970779. C220 859 (1) 4045891.267946153.72068132891. C233 861 (1,3,7,21,41,123,287) 10388827.20958338017.78390786811. .4423364633142650480377.11306831838018220372427161. .32215327209835441806959889495947251.P35 863 (1) 535070645969.176177196937327118084628312251. .605471410378222574753949751873375051.C183 865 (1,5,173) 29923811.60313752055701307811411. C178 867 (1,3,17,51,289) 679015215511191577.5913950382316342222561.P125 869 (1,11,79) 15643.27809.140779. C222 871 (1,13,67) 9168220907.2085976638755288150171.57604499880518482364227.C185 873 (1,3,9,97,291) 1747.22699.921446320166308603. .435350962502860533102854399065360163787224236964302573321.P92 875 (1,5,7,25,35,125,175) 558251.10022251. C168 877 (1) 29819.42355831233323.18969179136276645172100272388219. .5493451945310865752349090299716764102827.C175 879 (1,3,293) 42193.P172 881 (1) 22907.58147.70481.149771.42295049. C238 883 (1) 21193.294923.4675171089162696937.P237 885 (1,3,5,15,59,177,295) 516266521.873791632531.2354488203481.P107 887 (1) 5323.2607411387302489.118667786561338086904896542913501309901939.C207 889 (1,7,127) 19901547974019072445900746812468273. C194 891 (1,3,9,11,27,33,81,99,297) 7129.352246478761.620617419930817. .1409033313878253109224688819.236552624101029630306294196057.P76 893 (1,19,47) 1787. C247 895 (1,5,179) 14321.121721.145560017652641.10430557104202241. .5070463106922154841.1678434450877307861649130441. .298360269108491443679449696455011.P97 897 (1,3,13,23,39,69,299) 21529.258337.66354530124557299. .31735484991529375057.8437649245385270023387.P91 899 (1,29,31) 21577.69948188740643.127802493095470979. .575087607870890436346963910799123377.P182 901 (1,17,53) 105108859.P243 903 (1,3,7,21,43,129,301) 5757529.7243867. .378717376673487267097266291431316313.P103 905 (1,5,181) 127002291721. C206 907 (1) 8156908781432775187914049.292694927386576695497498001026561.P216 909 (1,3,9,101,303) 9091.11312395373674587455280184557176229738187. .7566725580973124820814763156483276883350707.P94 911 (1) 830833.346637323.P260 913 (1,11,83) 2389059505456889. C232 915 (1,3,5,15,61,183,305) 19895761.3015049441.288842216366491. .68207639734963563361372213456131836731.P76 917 (1,7,131) P235 919 (1) 14968673.2014093267.4317704341862180531. .185245489299285834957735107.P215 921 (1,3,307) 24365977.31992843313. C167 923 (1,13,71) C254 925 (1,5,25,37,185) C217 927 (1,3,9,103,309) 61339736467.395125276559977.11372732144384815780057.P137 929 (1) 8243947.3706175321483.389593452245969.489624750530873. .152118805170622193260551601681.8082308165748527072282228058900817.P168 931 (1,7,19,49,133) 5684313601.420502918802525203. .5714479757812584606479198276300869021129.C161 933 (1,3,311) 1867.121291. C179 935 (1,5,11,17,55,85,187) 7481.22441.192611.4942411.96162881.P165 937 (1) 1431737.20795779.40172939.1961075885814321323. .2007828853899141769868082345131291.P209 939 (1,3,313) 35534561977.2492985246309625270804406373331.P148 941 (1) 1738969.5062155107501579.1053336016261649316809.P240 943 (1,23,41) 1484493554507.28554501136089979495033. .1112321273705537423158810077602360080577.C192 945 (1,3,5,7,9,15,21,27,35,45,63,105,135,189,315) 69931. .535027074087349862035936711342201.P93 947 (1) 7577.13259.91254170041.212341461377.881206290008086216099. .23016485461806757328483.C212 949 (1,13,73) 182209.42598203337. C245 951 (1,3,317) 1480727923. C182 953 (1) 1907.425796183929.1624700279478894385598779655842584377. .3802306738549441324432139091271828121. .128064886830166671444802576129115872060027.C158 955 (1,5,191) 2766037497160081. C214 957 (1,3,11,29,33,87,319) 246907.2398243.143241922561. .3106925099920735897.P128 959 (1,7,137) 1726201.14590250979416323.29446854121733451929.P204 961 (1,31) 12787096753.845740940776943899258211. .22340510647512915642585947.C221 963 (1,3,9,107,321) 3156148413859611691.P174 965 (1,5,193) 1931.30881.37420771.5725218872819272688156683843001.P186 967 (1) 440953. C285 969 (1,3,17,19,51,57,323) 1932620113. C164 971 (1) 495211.3019967621847401.745797773625002825025979. .2491229639091384610638595922517649613788649.P205 973 (1,7,139) 15569.490393.1738265567571623156365340866047578896250851.P198 975 (1,3,5,13,15,25,39,65,75,195,325) 386263879315103401. .136676778088193015037036862018432177034334500891572775415001.P68 977 (1) 7817.728843.7128193.9524716048809932689.P259 979 (1,11,89) 39161.585443. C255 981 (1,3,9,109,327) 17659.295188787.96761365841467. C169 983 (1) 880060241.6692446515577.450533013876830977899721147965761959561.C236 985 (1,5,197) 1512961.42136857550241.259101467678452891. .1212008606838635171.5004132468697940487346607403971.P151 987 (1,3,7,21,47,141,329) 5135123689810129.51548005944477448439636\ 19802983305243869440153396482199500404535444787331.P78 989 (1,23,43) 1979.49451.14407753.197443880998681. C249 991 (1) 3060209.5819153.3122895040527689387017. C264 993 (1,3,331) 1987.25819.75904445347. C181 995 (1,5,199) P239 997 (1) 614153.27557081. C287 999 (1,3,9,27,37,111,333) 23977.5814899281.97377658867. .241947707873451279499.P150 1001 (1,7,11,13,77,91,143) 66067. C212 1003 (1,17,59) 21014857.P273 1005 (1,3,5,15,67,201,335) 14908171.P152 1007 (1,19,53) 169177. C277 1009 (1) 962587.39865023275343572161.9950355017715631542984016422092411.C244 1011 (1,3,337) 37760873163247728235828372169734753939. C165 1013 (1) 2027.14284942415590523.2022033791466488360947.P264 1015 (1,5,7,29,35,145,203) 6091.316681.395851.4936961. .118310908116219234147550210872300654121. .134148838212903456989907164771379816790203241.P99 1017 (1,3,9,113,339) 146449.457651.28876407885213594067. C173 1019 (1) 31309721343425737972332358633. C278 1021 (1) 10211.18379.441073.63145268487193.2116429105836954764874673. .695060280235636196787387625147.C225 1023 (1,3,11,31,33,93,341) 6679688731. .809412655973078797084604039087771314939.P132 1025 (1,5,25,41,205) 4036451.142958801.1243595348645401. .26815123266670488105926669652266381711401.C171 1027 (1,13,79) 6163.16433.14983931.23908561.419502198233. .6500198488452063592176409.C223 1029 (1,3,7,21,49,147,343) 8233.36892437056956699. .17008283446306740920401868978031815852569.P117 1031 (1) 79445908023117847711350146066567930257.P272 1033 (1) 24651922299337. C298 1035 (1,3,5,9,15,23,45,69,115,207,345) 211104810001. .697174543237430742710277767082091045949449114019397091.P94 1037 (1,17,61) 23889800393.615240811219. C267 1039 (1) 155851.762642847088874611.15029302019723991462779685090903481.P256 1041 (1,3,347) 2083.14865481.7791024427430986498793899. C174 1043 (1,7,149) 17747689. C261 1045 (1,5,11,19,55,95,209) 6613335467116613731.21654734961841342681. .302830601299346947201.P158 1047 (1,3,349) 24474001921.P200 1049 (1) 2099.1779522099931.24132756641778030091. C281 1051 (1) 26015176530521.234166918021181298229848923411137491270809. C262 1053 (1,3,9,13,27,39,81,117,351) 10166476786129.93961711110587347.P166 1055 (1,5,211) 101281. C249 1057 (1,7,151) C272 1059 (1,3,353) 3286329043.117598477011619. .83787479610878510956478965630065403939.P151 1061 (1) 3428736325987808713.P301 1063 (1) 114584129081.26210488518118323164267329859. C281 1065 (1,3,5,15,71,213,355) 2131.67531050720249264044979244321. .160525888079920212258843748245804191445670399750291.P87 1067 (1,11,97) 8537.25705142292017.4282346827889826334464447699353. C242 1069 (1) 7681945177. C312 1071 (1,3,7,9,17,21,51,63,119,153,357) 6427.17137.119953.1340000929. .49697164752429114523. .1078825191548640568143407841173742460493739682993.P84 1073 (1,29,37) 34149299.723179476352802400636953428399129.P264 1075 (1,5,25,43,215) 6451.32251. C245 1077 (1,3,359) 25742490619.61965231619.489719099073327823465690986241.P165 1079 (1,13,83) 110059.28066418320592174976920728908193. C260 1081 (1,23,47) 1399100926820497.1729444049094495656521.P269 1083 (1,3,19,57,361) 2062835090323897.P191 1085 (1,5,7,31,35,155,217) C217 1087 (1) 121398914459.59015046142680340633.144288053938906556201. C276 1089 (1,3,9,11,33,99,121,363) 2779129.P193 1091 (1) 4176767728322304092689. C307 1093 (1) 306041.149076457.P315 1095 (1,3,5,15,73,219,365) 3241201.5665531.1005823201.24375654323161. .75585758834018224531. .8395287354754937404878748093233887467947014370925681.P66 1097 (1) 1237417.993889927170673797197063676220796827. C288 1099 (1,7,157) 116615439604018153.719246910720211929911689. C242 1101 (1,3,367) 28627. C217 1103 (1) 227219.20354222567550187.23531055927158473. .172634405376546547951628091436445763552227.C253 1105 (1,5,13,17,65,85,221) 44201. C227 1107 (1,3,9,27,41,123,369) 369560523547. C206 1109 (1) 314468041.4498094107721.114707191763959751382208987. C287 1111 (1,11,101) 15120619254845707358936819. .359846976075630863007498752386627.P244 1113 (1,3,7,21,53,159,371) 90972169.7400606817397019353. C161 1115 (1,5,223) 382557003061241. C253 1117 (1) 70533063399945787.P319 1119 (1,3,373) 326208643.30155506036528513. C200 1121 (1,19,59) 2243.6088599401.58142098448088409. .359071640268582342735956401.P258 1123 (1) C338 1125 (1,3,5,9,15,25,45,75,125,225,375) 9001.11251.130147868251. .2104496060760001.1911491848228371127909236272251. .19939338707834433467107535745725657572743352610488782001.P61 1127 (1,7,23,49,161) 7736786575986931. C263 1129 (1) 5297035427. C330 1131 (1,3,13,29,39,87,377) 61318393206415264609. .862129909267689232423274352672765463729913497.C138 1133 (1,11,103) 2267.12945659. C297 1135 (1,5,227) 7025651.685467361.1046622091.6156694758084075792273361. C223 1137 (1,3,379) C228 1139 (1,17,67) 195090954822051707. C301 1141 (1,7,163) 18257.301870128784337.1200893348906161. .722526146028558523.17060613539298460913312913761.P213 1143 (1,3,9,127,381) 2576323.2061165716371. .9403580927289288953072692831494040201.C172 1145 (1,5,229) 406225165149481.73563032256320682421346570851. .3762270397244577165640826633613851.P198 1147 (1,31,37) 305771849. C317 1149 (1,3,383) P231 1151 (1) 9209.264731.7183639052011.8057089084163503088491. C302 1153 (1) 27673.3772896236651.1815221738378898021554747. C306 1155 (1,3,5,7,11,15,21,33,35,55,77,105,165,231,385) 9241.18481. .113571560808091. .928267859145048237228203439064060384235841167452667731.P69 1157 (1,13,89) C319 1159 (1,19,61) 117466969. C318 1161 (1,3,9,27,43,129,387) 2779191397441. C216 1163 (1) 59301371.10534255862017.116877740332519011737292886104457. C297 1165 (1,5,233) 179411.9813961. C268 1167 (1,3,389) 9337.97484277202003.45908592787319236096963. .936622732283266044834451024147.C164 1169 (1,7,167) 2339.37409.161323.14608351671572807850092203. .8414160072705585053393085689.C234 1171 (1) 25763.84313.P343 1173 (1,3,17,23,51,69,391) 236947.647674297.4080494539544536849. C180 1175 (1,5,25,47,235) 185651. C272 1177 (1,11,107) 49504078597120643.166419727156424727241892848411. C274 1179 (1,3,9,131,393) 25939.82531. C226 1181 (1) 49603.59051.11403737.67685946763. .9186599509882727262279760862379532536049.P288 1183 (1,7,13,91,169) 18256533429955747955939. C260 1185 (1,3,5,15,79,237,395) 2371.18859377449506801.P169 1187 (1) 626523937064728884681163. C334 1189 (1,29,41) 28537.306763.9758744379744403.P312 1191 (1,3,397) 1819849.43247593.64339323043.427329609001. .66809564696120553953329.C180 1193 (1) 324497.6132176836553. C341 1195 (1,5,239) 184087361. C279 1197 (1,3,7,9,19,21,57,63,133,171,399) 778051.1697347.P183 1199 (1,11,109) 447252559596639611.298257415638476586139. .794144907494779140961.1996742176615621275047178653063503969.P230 Table 2LM Factorizations of 2^n+1, n=4k-2, n<2400 n Prime Factors 2 5 6 (2) 13 10L (2) 5* M 41 14L 113 M (2) 29 18L (6) 37 M (2) 109 22L (2) 397 M 2113 26L (2) 1613 M 53.157 30L (6,10M) 61 M (2,10L) 1321 34L 137.953 M (2) 26317 38L (2) 229.457 M 525313 42L (2,14M) 14449 M (6,14L) 1429 46L 277.30269 M (2) 1013.1657 50L (10M) 101.8101 M (2,10L) 5*.268501 54L (2,18M) 246241 M (6,18L) 279073 58L (2) 107367629 M 536903681 62L 5581.384773 M (2) 8681.49477 66L (6,22M) 312709 M (2,22L) 4327489 70L (2,10L,14M) 47392381 M (10M,14L) 7416361 74L (2) 149.184481113 M 593.231769777 78L (6,26M) 13*.313.1249 M (2,26L) 3121.21841 82L 181549.12112549 M (2) 10169.43249589 86L (2) 1759217765581 M 173.101653.500177 90L (2,10L,18M,30M) 181.54001 M (6,10M,18L,30L) 29247661 94L 140737471578113 M (2) 3761.7484047069 98L (14L) 4981857697937 M (2,14M) 197.19707683773 102L (2,34M) 409.3061.13669 M (6,34L) 1326700741 106L (2) 1801439824104653 M 15358129.586477649 110L (10M,22M) 415878438361 M (2,10L,22L) 3630105520141 114L (6,38M) 131101.160969 M (2,38L) 275415303169 118L (2) 1181.3541.157649.174877 M 5521693.104399276341 122L (2) 733.1709.368140581013 M 3456749.667055378149 126L (6,14L,18L,42M) 118750098349 M (2,14M,18M,42L) 40388473189 130L (10M,26M) 108140989558681 M (2,10L,26L) 521.51481.34110701 134L (2) 269.42875177.2559066073 M 15152453.9739278030221 138L (2,46M) 70334392823809 M (6,46L) 5415624023749 142L 4999465853.472287102421 M (2) 569.148587949.5585522857 146L 9444732965601851473921 M (2) 293.9929.649301712182209 150L (2,10L,30M,50M) 63901.13334701 M (6,10M,30L,50L) 1201.1182468601 154L (2,14M,22L) 869467061.3019242689 M (14L,22M) 8317.76096559910757 158L 604462909806215075725313 M (2) 317.381364611866507317969 162L (6,18L,54M) 3618757.4977454861 M (2,18M,54L) 106979941.168410989 166L (2) 13063537.148067197374074653 M 997.46202197673.209957719973 170L (2,10L,34M) 1021.4421.550801.23650061 M (10M,34L) 7226904352843746841 174L (6,58M) 22170214192500421 M (2,58L) 349.29581.27920807689 178L 1069.579017791994999956106149 M (2) 123794003928545064364330189 182L (2,14M,26L) 1093.1093.8861085190774909 M (14L,26M) 4733.556338525912325157 186L (2,62M) 4611545283086450689 M (6,62L) 373.951088215727633 190L (10M,38M) 761.2416923620660807201 M (2,10L,38L) 54721.276696631250953741 194L 389.4657.4959325597.17637260034881 M (2) 3881.5821.3555339061.394563864677 198L (2,18M,22L,66M) 42373.15975607282273 M (6,18L,22M,66L) 235621.8463901912489 202L (2) 9491060093.53425037363873248657 M 809.5218735279937.600503817460697 206L 41201.520379897.473000157711296729 M (2) 17325013.117070097457656623005977 210L (6,10M,14L,30L,42M,70M) 1041815865690181 M (2,10L,14M,30M,42L,70L) 421.146919792181 214L (2) 857.37866809061660057264219253397 M 843589.8174912477117.23528569104401 218L (2) 74323515777853.1746518852140345553 M 5669.666184021.171857646012809566969 222L (6,74M) 1453030298001690873541 M (2,74L) 3109.1398316729.4345052821 226L 10384593717069655112945804582584321 M (2) 58309.2362153.15079116213901326178369 230L (2,10L,46M) 461.5981.359006912765190408181 M (10M,46L) 15096281.1021622741.7834788541 234L (2,18M,26L,78M) 7489.370244405487013669 M (6,18L,26M,78L) 21061.348661.1112388285061 238L (14L,34L) 2381.42841.823481.536296539263941 M (2,14M,34M) 9521.18292898984156916156396101 242L (22M) 3389.91961.4036962584010807014809213 M (2,22L) 1339272539833668386958920468400193 246L (2,82M) 802333429.6027043735173469 M (6,82L) 2953.125965976976392564317 250L (2,10L,50M) 5*.28001.96001.94291866932171243501 M (10M,50L) 7001.3775501.47970133603445383501 254L 509.26417.140385293.90133566917913517709497 M (2) 18797.72118729.2792688414613.8988357880501 258L (6,86M) 5951631966296685834686149 M (2,86L) 17029.46957.96758771543686753 262L (2) 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C191 M (14L,218M) 228901.89585357.1193769557014682568929. .26949677948560956418555434041273937193. .58023940775396337496088317549973016234295004562061.P74 1530L (2,10L,18M,30M,34M,90L,102L,170L,306M,510M) 36721.70381.965133181.P98 M (6,10M,18L,30L,34L,90M,102M,170M,306L,510L) 253190737566001. .358689400191468213568189014966376501.P66 1534L (26M,118M) 2602289873.14878594277.697288564688146289. C172 M (2,26L,118L) 32554549.1301673138221.1391657728553.10261059495917413. .174574320633190844334669825437.C133 1538L 1508116661.728725553653.P211 M (2) 487854440461236965376721. C208 1542L (2,514M) 293171209.7752412975359697.340066554311536965308417882742061.P98 M (6,514L) 552218538342469. .6085412460587930083903553583244932908333069728961100695226000917581.P73 1546L (2) 9277.961613.8979169.28764877.1286673961.6144001889.20680804897. .72888144455528365833889.101159392465333020291272490553669.P124 M 8950276336541.P220 1550L (10M,50L,62L,310M) C181 M (2,10L,50M,62M,310L) 106288917242483907573395401.P155 1554L (6,14L,42M,74M,222L,518M) 15541.P127 M (2,14M,42L,74L,222M,518L) 21757.P126 1558L (2,38L,82M) 65437.2841793.3745809992085397.P191 M (38M,82L) P217 1562L (2,22L,142M) 257068815787496849489.P191 M (22M,142L) 12497.777877.1462033.1668464524433015165835133. .1072443701632072579384549789.8247505706276398056121502653493.P113 1566L (6,18L,54M,58M,174L,522M) 1005373.900238389553.88293718850941.P120 M (2,18M,54L,58L,174M,522L) 18793.121571536007648069609869.P125 1570L (10M,314M) 1814921.2704723867921.35422803263041.P156 M (2,10L,314L) 762464332510640867293939564541.P159 1574L (2) 26940527389021586346998869. C211 M 47221.406093.14121929.P220 1578L (2,526M) 104530192048153.89278383816591944174173. .468320479654392916258882359560461. .35467094651948541600331422014320230649.P52 M (6,526L) 177592095535805413. .209464891971049544444372157566739020805493.P99 1582L (14L,226L) 113*.6329.94395483835364237.362648335437701461. C162 M (2,14M,226M) 85429.116163097.P190 1586L (26M,122M) 582049312001.26969455685328761021. .502340346136939736695391222101.C156 M (2,26L,122L) 179846057.47708294713.3385836026574025144947910893473.C168 1590L (2,10L,30M,106L,318M,530M) 27087241.1373040346921.5284407007801. .1210269871632394075226641.683607720175140192010111693752601.P36 M (6,10M,30L,106M,318L,530L) 19081.184441.2422984469411281887781.P95 1594L (2) 2097515909.364129241317395157.P213 M 1131019499249.P228 1598L (34L,94L) 41549.290837.7142332055234648333.6099217213901879740081. C171 M (2,34M,94M) 51137.5394672221. C208 1602L (6,18L,178L,534M) 6565668841.1539976855861.72911451369675792637. .3945245703312222053852257.P93 M (2,18M,178M,534L) 14170974714403144763101597.P134 1606L (2,22L,146M) 50219621.1808418581560889.903888164009442693590288077. .1482338506032222870906022459128577.C135 M (22M,146L) 19273.2862083701562715653. C194 1610L (2,10L,14M,46M,70L,230L,322M) 158149013123372670109481. C136 M (10M,14L,46L,70M,230M,322L) 6216303835549501.P144 1614L (6,538M) 416413.2621137.962643846199733408565200877781060429.P113 M (2,538L) 16141.30701107729.43932915373.1868171919242953. .914570427675304311896510460383772935570463409.P77 1618L C244 M (2) 6473.25889.1948073.7660242424577. C216 1622L (2) 226993790701.120375361925202961.P215 M 5336381.1178063188140768549097. C217 1626L (2,542M) 273883482277.2486873948884993.198779717698841035284255913. .1661993671243438017256281256149910093.P74 M (6,542L) 3253.78049.1593481.1475273053.83478798429270328887973. .73044219855003574103778189733. .4713405292661216398984672353497652737173.P47 1630L (10M,326M) 45641.196239297090446416678541. .3707642406570829114833393150344141.P134 M (2,10L,326L) 9248621.7627588261. C179 1634L (38M,86M) 2091521.15886294883461.5285748520741386282105949513. .11811951218548871673638976031338702013.C143 M (2,38L,86L) 382357.6052337.6483713.11637349.17147197.P195 1638L (2,14M,18M,26L,42L,78M,126M,182L,234L,546M) 507781.6224401.P118 M (6,14L,18L,26M,42M,78L,126L,182M,234M,546L) P130 1642L (2) 441085379960554789.356378849959441965290887469317261822121. C191 M C248 1646L 19753.17678041.28473240575821815736340752613. C208 M (2) 924509587369596772157.P227 1650L (6,10M,22M,30L,50L,66L,110L,150M,330M,550M) 164342074315726836781988740273689592246064114457301.P71 M (2,10L,22L,30M,50M,66M,110M,150L,330L,550L) 42217104570301.P107 1654L (2) 36389.148861.2312293.130582063447518110584062446171193488957. C195 M 50493458584097.291599907662880149. .1850744891824232892018330060023474649953.C179 1658L (2) 464235512584146182617.479329249434015760837735948908881. C196 M 3825173678485409449.7983838621160200177.12624459932825972330038421.C187 1662L (6,554M) 9973.1125470603488333.51689114452666429. .676569636302657152854889.487914335884174463488431988112971564897.P68 M (2,554L) 171028625446956073.P150 1666L (14L,34L,98L,238L) 16661.46649.1868371709557081.20378049054645577. .199344004099971410597.C142 M (2,14M,34M,98M,238M) 73500589.26980673413.440703752018377.P170 1670L (2,10L,334M) 430861.3154569881.7846415030381.22625604968060184427321. .2262086882766687062334641.P126 M (10M,334L) C200 1674L (2,18M,54L,62M,186L,558M) 70309.4081213.1297451663483880043725\ 856297294610187704362366686186248013808494382873.P83 M (6,18L,54M,62L,186M,558L) 789059989.P154 1678L 5564249.2793879899538857933.19338500498002810228771062564557. C197 M (2) C252 1682L (58M) C245 M (2,58L) 366677.3727313.13866300353.213360835453.1127518158768077.P196 1686L (2,562M) 2206057267849. C157 M (6,562L) 5999663863513.P156 1690L (2,10L,26L,130M,338M) 1165339501.333398126078661934421. .10951196901534534492850755810091411261. .8500591978242473249929589155637812362821.P82 M (10M,26M,130L,338L) C188 1694L (14L,22M,154M,242L) 29018221.343251023344259430080136457. C165 M (2,14M,22L,154L,242M) 908695481.6202401437.13560087157. C170 1698L (6,566M) 3830689.53028541.45039969589.2403898139108413. .96943448874943589381509.P106 M (2,566L) 526381.2212378537.113620361303857.P142 1702L (2,46M,74L) 450395984739049729770917.P216 M (46L,74M) 3466225121.P229 1706L (2) 3413.64007056091437.1122047772459197542365557. .3670300973252073917081977.P191 M 57568727236201. C244 1710L (6,10M,18L,30L,38M,90M,114L,190L,342M,570M) 110017981.848129221.P113 M (2,10L,18M,30M,38L,90L,114M,190M,342L,570L) P131 1714L 4702664630197.6871169125116761.8859671727690991421. .51158163991710264101.C191 M (2) 7490495630917903672489.1112610919806658266406382986993. .37254915681318275345339031340236801161.C168 1718L (2) 82488053.160783317963711097. C233 M 41233.18970157. C247 1722L (2,14M,42L,82M,246L,574M) 2675989.P138 M (6,14L,42M,82L,246M,574L) 44773.82657. .11226524876408775073143033704082858121.P99 1726L 62137.7682681449.12118208029.7636302550869852997. C217 M (2) 12268162909.4190110941193.41734812223623741861146169997. .46619255366962328167412700221.406766837212504479804114509779153.C147 1730L (10M,346M) 13841. C203 M (2,10L,346L) 3461.297197052517429014237901. .155239988274216593089164596199061.P149 1734L (2,34M,102L,578M) 3469.38149. C156 M (6,34L,102M,578L) 83233.67133458080301.15286531841496313. .76087114479348013.P112 1738L (2,22L,158M) 79976245841124049692014336050829.P204 M (22M,158L) 10429.59093.794450909331238272563227097.P199 1742L (26M,134M) P239 M (2,26L,134L) 482919699751741253.P222 1746L (6,18L,194L,582M) 376885109765881657.P157 M (2,18M,194M,582L) 19181586049511261238746281.41438480715993428\ 32189552657193683851218149055132998865238029290237501.P79 1750L (2,10L,14M,50M,70L,250L,350M) 21001.90984652501.259213867501. .66769116536501.P141 M (10M,14L,50L,70M,250M,350L) 52501.304501.P171 1754L (2) 136813.16485685958318067491706639165873936208073.P218 M 178909.8045864609.94177931835255001. C232 1758L (6,586M) 3517.17581. C168 M (2,586L) 70321.3681253.1465751310316457222898312721. .786189125604290817435554536817956201.P102 1762L 292493.287799987821. C249 M (2) 9908497304929.3070352086706435689. C234 1766L (2) 3533.10597. C258 M 9642835106981.21853773066679313.1397997900714226472761369661333. C207 1770L (2,10L,30M,118L,354M,590M) 941641.112688376490130041. .13958078871765695340080761.P91 M (6,10M,30L,118M,354L,590L) P141 1774L 1982764321.9982363219299701755701813517. .2047754087000820349297809443743844453329. .13231286310635194760975216003886759010777.P151 M (2) 12067954321.154247171201.246306661383223563619590775949. C216 1778L (14L,254L) 394717.2901290617. C213 M (2,14M,254M) 3557.430277.28402945481. C209 1782L (2,18M,22L,54L,66M,162M,198L,594M) 120726937.212140766502632881. C138 M (6,18L,22M,54M,66L,162L,198M,594L) 2170477.168518034037. C145 1786L (2,38L,94M) 3639869.999648574070171124601432769. .497403465856372009446461144453. .111758423615256944193654963749427567569.C149 M (38M,94L) 646109108522520037.55737216228051297161494379261805713.P197 1790L (10M,358M) 3581.811893881.4272700190724544357721. .682862187512541058734549287082001.P147 M (2,10L,358L) 94622981.9818823675183373550041. .671277176269260334004380493401.C156 1794L (6,26M,46L,78L,138M,598M) 7177.P156 M (2,26L,46M,78M,138L,598L) 10684568857. C149 1798L (2,58L,62M) 7193.3617439859037.8713454341549.109097329238284141. C207 M (58M,62L) 5886653.20723877457.43875868248089. .39574364572001586424595746349.C194 1802L (2,34M,106L) 11747392973.91102528862545665457.P221 M (34L,106M) 174044748410668549457.224201551150113268933.P210 1806L (6,14L,42M,86M,258L,602M) 3613.9467360568830697495500595457. .45757320478618895747604607889547060541.P83 M (2,14M,42L,86L,258M,602L) 44619686161. C141 1810L (10M,362M) 1422661.10371301.62984381.2841546437106680644141. .100673282665910769164456015319401.P142 M (2,10L,362L) 4779887821.284960538160486454165307301. .1486018607888551051882493975787406621.P145 1814L (2) 36684968468392674349.267301538121080056247956934369.P224 M 2856279634519890658989627576084877545889. C234 1818L (2,18M,202L,606M) 938089.215403913.54459411697.P156 M (6,18L,202M,606L) 3637.11239182354817.89718779799289.P151 1822L 109321.42514235518096149015446235113. C241 M (2) 29153. C270 1826L (22M,166M) 10957.457905185813813.9118425814963735020084050069. .758984045239765414366290480154514089.C164 M (2,22L,166L) 437342857760433461.31722291643604475850861201188341. C199 1830L (2,10L,30M,122L,366M,610M) 1712881. .209286094074580318288344692937218868614221.P97 M (6,10M,30L,122M,366L,610L) 61*.358681.602914116781. .2397096504835438921.89135366684453039762936076301.P79 1834L (2,14M,262L) 18341.73361.106373.337457.602481460214341. C201 M (14L,262M) 55021.11142479091341921.96578697208818436822981. .730039745374219638260113.37447027901314381254512721318017. .639745584291728863751658159947413.P103 1838L 15174529.1508449364353. C258 M (2) 3677.169097.2703022685717.1071847300685268733. .2456774736627079417449898904657.P207 1842L (6,614M) 2903157652807014132222997.P160 M (2,614L) 14737.202621.670489.1924167937.20277440672157064961857.P138 1846L (2,26L,142M) 38286041. C246 M (26M,142L) 13837693811900871607717600062424369. C219 1850L (2,10L,50M,74L,370M) 3701.133886258536001.590663067860911343898701.C176 M (10M,50L,74M,370L) 3760458001.9312718358338301.P192 1854L (6,18L,206L,618M) 401841732395629.10017165502306460200391243108137.P139 M (2,18M,206M,618L) 3709.7417.93097809073. .15697920117275073486338469567634384633.P129 1858L 11149.319577.551019709753.4609832458707079151039619761. .1020789673987483714669438485415945837.P195 M (2) 7433.85469.858397.P265 1862L (2,14M,38L,98M,266L) 4639388993.22772885633.114089637061. C197 M (14L,38M,98L,266M) 11173. C224 1866L (2,622M) 3733.17962117.204082834247639533. .2867134239058725077444870925351109. .171787846178241745388291751687545359135893624733.P79 M (6,622L) 14929.31582002281292084633680717617.P154 1870L (10M,22M,34L,110L,170M,374M) 706960763753201. C179 M (2,10L,22L,34M,110M,170L,374L) C193 1874L 546289747242387833.102338449889938893229. C245 M (2) 802073.30214971197129.524704862656309.108215387436410988313.P228 1878L (2,626M) 3651421693.153204659721481575760771776889.P150 M (6,626L) 120193.23208500533.484894051077157.479542202751565609741. .21514288711632793647440840947984309.P103 1882L (2) 3383837.25359946237.20793657827081209534512961080066477973.P229 M 1070913479895698609. C266 1886L (46L,82L) 112410858169.36368413831997333.P237 M (2,46M,82M) 2784254414828346243382561. C241 1890L (6,10M,14L,18L,30L,42M,54M,70M,90M,126L,210L,270L,378M,630M) 7561. .457381.2143261.596526861195233662750200340726624395569101.P73 M (2,10L,14M,18M,30M,42L,54L,70L,90L,126M,210M,270M,378L,630L) 43887888187572165151544641.53557082595126165043094157045628806518641.P64 1894L (2) 189401.1440383213.8204616582857089246514152381.P243 M 6522937.272279643245537.8211191052325823017421025141068065597. C227 1898L (2,26L,146M) 10390402230053.185571869124044164853371079021. C219 M (26M,146L) 3797. C257 1902L (6,634M) 2892776771209447770340654201.P163 M (2,634L) 15217.31877128189.778680603097.3488331309973. .27069571592372896954201.P130 1906L 20405494957.P277 M (2) 2809306768001. C274 1910L (2,10L,382M) 1443961.92459281.P216 M (10M,382L) 57301.864189637596221.301039635955941955416398544601. C180 1914L (2,22L,58L,66M,174M,638M) 840440400036193222729. .1085449968759125093329919224369. .1585333835462829231438151788148865056453.P78 M (6,22M,58M,66L,174L,638L) 15313. C165 1918L (14L,274L) 7673.609014465221.5055546728233. C218 M (2,14M,274M) 168388835672177. C232 1922L (62L) 1137450670721.2184269724947805073. C250 M (2,62M) 252792973.864219613.948729953.37541358506075478258236735332361. .64570584168627945448109624328792927541.C185 1926L (2,18M,214L,642M) P192 M (6,18L,214M,642L) 3853. C189 1930L (2,10L,386M) 1246781.1608921341.3568553151401081. .5955623568140770033895876543735621.P168 M (10M,386L) 232492081623941.8392710322562681. C201 1934L 328781.12056557.P279 M (2) 47054221. C283 1938L (6,34L,38M,102M,114L,646M) 3877.19381.1279081. .12774353393983945521795713234563738297. .16750182073211230556310395420299476529.P86 M (2,34M,38L,102L,114M,646L) 926282517007889243128982867521. .3648011488087216916950150682966398143704581.P101 1942L (2) 5877612181049269.6917838004568007880938360151147285081.P239 M 19421. C289 1946L (2,14M,278L) 38921.87632273.92220941.44849676017189. .2684356809244885929794686184069.C186 M (14L,278M) 218561316364553. C235 1950L (6,10M,26M,30L,50L,78L,130L,150M,390M,650M) 24457095001.P134 M (2,10L,26L,30M,50M,78M,130M,150L,390L,650L) 45984901. .1131816004801.108792457407671701.P108 1954L 36716449417.415313933724293297909.P263 M (2) C294 1958L (2,22L,178M) 10984381.1749046157.12769069589. .8540463790853686106162888141.P211 M (22M,178L) 3917.4135297.21467513.57717951413.290857646356157.P222 1962L (2,18M,218L,654M) 109*.17951056093.669657070334773.P168 M (6,18L,218M,654L) 49346313013.1388612680921. C173 1966L 43644426217789.1431746688753709.P268 M (2) 155837128987432356781.1366175048897551662825186361. .1323103760614147332897213698137697413.P212 1970L (10M,394M) 15761.35461.2214281.464568607149275146234181. .581887899470864922007450289381.C168 M (2,10L,394L) P237 1974L (2,14M,42L,94M,282L,658M) 57174937.28860857283150817.P142 M (6,14L,42M,94L,282M,658L) 61706836445096809.P150 1978L (2,46M,86L) 7876397. C272 M (46L,86M) 439771371096041.35049840713898433. .46336564105264156931219140569625359563486333.C203 1982L 47569.702972273668806189.24108966487910875313. .44229415926893141209.113447996363645096441.P217 M (2) 27749.63488677307778109.16825619625747922745475011329. C249 1986L (6,662M) 13302229.25430936011753.31614476989231029379232557. .68905970337561183437462555868709.3973921258176323056321508940165661. .1314098716175595483898139799716487493.P51 M (2,662L) 183625814209.1018768450523377.74519189014953913. .18989372631177034732892899753.465177286996430226160539394957. .617680057559525522778680709413533.P66 1990L (2,10L,398M) 250741. C234 M (10M,398L) 23198204725672081034655436981. .36016148355139711248940080869144201.C176 1994L (2) 3989.23929.1316041.7905228953.450516200430246120721. .149156643181299310192264307577506850757.P217 M P301 1998L (6,18L,54M,74M,222L,666M) 72354413161.1222553230560433. .5735551460378502198796512243143473. .5497368458116180193233404694623299228824873.P93 M (2,18M,54L,74L,222M,666L) 10126001691430741.382598228266336189. C162 2002L (14L,22M,26M,154M,182M,286L) 20021.1849849.690545857. .41080280592351540541.9215194846651389888428137. .3969862289663363742872134096701517. .13628840986604456625675621031891749568696694946387077.P68 M (2,14M,22L,26L,154L,182L,286M) 8009.12039884736627749. C197 2006L (2,34M,118L) C280 M (34L,118M) 4013. C276 2010L (2,10L,30M,134L,402M,670M) 1161781.43714589671758035101. .7202139206809052400714203227736498330521.P93 M (6,10M,30L,134M,402L,670L) 4021.655261.13154273408381894504101.P129 2014L (38M,106M) 23704361089.2345207504177.44598149829737613346817.P237 M (2,38L,106L) 2211373.2743400324920929934072747900058453.P243 2018L 12109. C300 M (2) 242161.952957298276617. C283 2022L (2,674M) 8089.3546589.2922737792281.3181075216261429729586653.P156 M (6,674L) 737267931919513717708801. .397490855733113630613348630003685291009. .170970754136725722159939805266417998571170101.P96 2026L (2) 33449261.264484004729713012553.399321186049288505641. .956936627523697040100248003877237301005401.P214 M C305 2030L (10M,14L,58M,70M,290L,406M) 613061.85597365805801531151405792561041.C165 M (2,10L,14M,58L,70L,290M,406L) 36541.357281.P192 2034L (6,18L,226L,678M) 4077850171122577. C187 M (2,18M,226M,678L) 856216369.318132015893843401. .21147271559400204090224749.454399800958030464217761866249437. .1065856403671528263525870130273753.P85 2038L (2) 61141.207877.7150897365985729.223030353552686687144432969.P254 M C307 2042L (2) C307 M 88557457. C300 2046L (6,22M,62L,66L,186M,682M) 4093.10308836566117.909262501760934950641.C144 M (2,22L,62M,66M,186L,682L) 431919189109.45982033644093624122893.P146 2050L (10M,50L,82L,410M) 656400720309944201. .39701639943363232352915408020280101.C189 M (2,10L,50M,82M,410L) 3527365301.P232 2054L (2,26L,158M) 308101.24775349.105748241031224273. .24187837105009092776233550365107217.P218 M (26M,158L) 4828050703567261.P266 2058L (2,14M,42L,98M,294L,686M) 127597.7687554960386019181. .52003770991385964409.2258564379815977498898119074673. .359714423380600478940340236904806333157.P65 M (6,14L,42M,98L,294M,686L) 3346309.5417007821989854721.P152 2062L 181457. C306 M (2) 32993. C306 2066L 622097393.1606410037.2302309768953616705880653781. C266 M (2) 4133.78509.764610073. C293 2070L (2,10L,18M,30M,46M,90L,138L,230L,414M,690M) C160 M (6,10M,18L,30L,46L,90M,138M,230M,414L,690L) 12421.45541. C150 2074L (2,34M,122L) 8297.4674797.14475794101.9515330527620650472517. .423082350292474675079511971763937.P215 M (34L,122M) 24889.67591661.19245413381. .28507675395016426209379265459437.108418776698113814016172668034087889. .29372667805516620161464001230063579445161.C160 2078L 4157.47577889.25782331522951529761073.507644488024787734242019373. .144881493240241900269232403148013.C221 M (2) C313 2082L (6,694M) 6071113.42288273231097.920711247257749.56229065675693116237. .23384866763414531770204088484887647243643341. .6212208498791522443680860464057886551642074217423393.P58 M (2,694L) 8329.112429.1557337.592686737569.6867574890898053457.P164 2086L (2,14M,298L) 12517.33377.198857827144683169. .1926620590033512371166117610796118373573.C203 M (14L,298M) C268 2090L (2,10L,22L,38L,110M,190M,418M) 6029645821.P207 M (10M,22M,38M,110L,190L,418L) 1414585500587719775570810281. C191 2094L (6,698M) 2065299637.40562442707197.9617687207378317.P171 M (2,698L) C211 2098L 4640777.83011968817. C299 M (2) 12590854756648551516684021495487769. C281 2102L (2) 92489.2030533.207619855320079870004881. C282 M 1513441.77933753.120003217560112501.P286 2106L (2,18M,26L,54L,78M,162M,234L,702M) 511421041. C187 M (6,18L,26M,54M,78L,162L,234M,702L) 150937180544593. .23640543396721742414157469.P156 2110L (10M,422M) 7313261.1060955698661.8207774689941937459483922881.P206 M (2,10L,422L) 274301.163031261.3518920881831461. .7798241026129503827660037110146961.C191 2114L (14L,302L) 3646092601989001186525363589. .46407610276467440780784332348683797989.P206 M (2,14M,302M) 4229.9817417.13093972249.252329098404058364830457653. .1063976134790213153556087433.C198 2118L (2,706M) 1559123581453.80422923777405534042337. C178 M (6,706L) 27503548942141.2885299533969327285608778291701629.P165 2122L (2) 49459577.2308766446154677.P296 M 43497479736983828850647753.P294 2126L 4253.119057.2351357.118640804957.P294 M (2) 6262064969.51799226966893295289509.51114358532758153182876066459473. .1603777152900827521607976402498110749.C219 2130L (6,10M,30L,142L,426M,710M) 4261.46861.149101.775548522986795641. .14434789001414900976541.P116 M (2,10L,30M,142M,426L,710L) 8521.9883201. .935670834191020341514842275817603083341. .805863337960228852951520597182877664103305518701.P71 2134L (2,22L,194M) 819457.P284 M (22M,194L) 115237.8670835642148979210715595043749314093.P247 2138L (2) 25657.120995596673449.39769515373402823701741. .25628302455269700936935750561.P252 M 9900693519731369541341.59623715903776666409686137682448042581.P263 2142L (6,14L,18L,34L,42M,102M,126L,238L,306L,714M) 94655375162339953175243922917053.1678012401109759349697111520625113. .108843028104327227902725329813334696855127583727517.P58 M (2,14M,18M,34M,42L,102L,126M,238M,306M,714L) 4198321. C168 2146L (58M,74M) 5240533.1179926597.258921638441.6899099304599325137. C258 M (2,58L,74L) 10554029.17507069.4139856422575882915981. C268 2150L (2,10L,50M,86L,430M) 7480658401.P243 M (10M,50L,86M,430L) 4841801.8395496206695366401. C228 2154L (2,718M) 8193817.P210 M (6,718L) 4133482921.198349540321842343265473158857156629. C171 2158L (26M,166M) C296 M (2,26L,166L) 1281853.4683241262952304822589. .1216869644819515145377777.C245 2162L (46L,94L) 12973.1522049.10797029.777589754233.144244914186471029. C258 M (2,46M,94M) 84032617. C298 2166L (2,38L,114M,722M) 108301. C201 M (6,38M,114L,722L) 5716032168945734981112301013351337476653.P167 2170L (2,10L,14M,62M,70L,310L,434M) 156241.3670177421. .147099130461475017366732184489051451254241.C161 M (10M,14L,62L,70M,310M,434L) 34721.399281.16999781.54627581.P192 2174L 18241890517.28221633169.4792343120992181.6215871883210370333. C273 M (2) 4349.182617.887735509. C309 2178L (6,18L,22M,66L,198M,242L,726M) 7692697.158914152241813. .755084486042964623053695739861.P148 M (2,18M,22L,66M,198L,242M,726L) 4357.1028017.21366181. .1057452633848904633973879093.P155 2182L (2) 13093.2305837815915297883997398826188721.P291 M 2070456161.1206850555657249.475989046121563895183917. C281 2186L (2) 13155349. C322 M 4373.2680084093.7650524153545491153109. C295 2190L (6,10M,30L,146L,438M,730M) 250975213261. C163 M (2,10L,30M,146M,438L,730L) 4890608660294663498626741.P148 2194L 4541645821.87894343384213957. C304 M (2) 114089.79321877.27244396967751097. C301 2198L (2,14M,314L) 4397.35062794955017836596752826831321813. .2659583415856042053163877781991246706041.C205 M (14L,314M) 30773.3064013.P271 2202L (2,734M) 40201011439837.3831232706825413.374900727248428800313. C172 M (6,734L) 7170258097.P210 2206L 132361.23687834930522629.1028852979752817834773. C290 M (2) 525029.37191616185794836393.697490210515755486688501. .165918875741241072476219693.C256 2210L (10M,26M,34L,130L,170M,442M) 9007961.59234660941.31795116701141. .323741938065360073352861.P177 M (2,10L,26L,34M,130M,170L,442L) 113850361.4067383975981. C211 2214L (2,18M,54L,82M,246L,738M) 756004316065821564119228881. C190 M (6,18L,54M,82L,246M,738L) 36336169. C210 2218L (2) 13309.3828205897.6295438698503197. .65811083601260126519272378671163489.C269 M 115337.884194242639628957.435014425521838380022061. .31278302767943794898000377.C262 2222L (22M,202M) 17353692547269107417712398470333081. .600642331003578944290343659354472393377.C228 M (2,22L,202L) 679933.10576721. C289 2226L (6,14L,42M,106M,318L,742M) C189 M (2,14M,42L,106L,318M,742L) 347257.286867892221.1057320723649. .301319905573933.C144 2230L (2,10L,446M) 16399421.87312813129989707389666674041. C232 M (10M,446L) 829561.1016881.81345941.74926147874622258725821. C225 2234L (2) 67021.250782329104747870229.280207617845230614289.P290 M 40213.71514809.P324 2238L (6,746M) 22381.29576255130269968537. C200 M (2,746L) 998556391921793032142257083493. .8188933824660612984535850181113325193.C158 2242L (38M,118M) 12041422327407135159361.5152358624818762552412257. C268 M (2,38L,118L) 341851193.P307 2246L (2) 40429.7224113271397534157.358944225239163622577. C294 M 4493.597437.1157722594009.5903190099601.24233759097340549. C288 2250L (2,10L,18M,30M,50M,90L,150L,250L,450M,750M) C181 M (6,10M,18L,30L,50L,90M,150M,250M,450L,750L) 1799059501.P172 2254L (14L,46L,98L,322L) 22541.108193.270889143560029. .11969933001079298510777.C233 M (2,14M,46M,98M,322M) 10651266956177.2796521796509427468413. .177440652731822006259181.P221 2258L 279811361.P332 M (2) 4517.31687253327909.845860743041780788841. .3168961980027270675772903049581441. .610169797505852063167912929664486129.P232 2262L (2,26L,58L,78M,174M,754M) 9049.153817.22203793.58775279454393529. C169 M (6,26M,58M,78L,174L,754L) 2232143146107248761501297.P179 2266L (2,22L,206M) 13597.5791897.41143843577. .10007965273275904867471368225133.C255 M (22M,206L) 90641.1319991045191762036137969.P278 2270L (10M,454M) 3979941061. C263 M (2,10L,454L) 514854161.1852360842230441. .11854787490285963159654548088590829070481.C209 2274L (6,758M) 245593.P222 M (2,758L) 451942901656777.507017710250042219226541.P190 2278L (2,34M,134L) 82009.2924953.7198481.702133429141. C289 M (34L,134M) 57610621.1026114653093.83181322758949952160061. C275 2282L (2,14M,326L) 13693.3340849.1999940237.5021162189. C264 M (14L,326M) 8734996205489.254089910482240077841. .193162081274292925141302977259421.P227 2286L (6,18L,254L,762M) 68581.30957013.24172568107332159475316053. .36983739239549519680341811045815130322384077.P147 M (2,18M,254M,762L) 18289.662941.2977460232013. C205 2290L (10M,458M) 18967080721.P264 M (2,10L,458L) 9161. C272 2294L (2,62M,74L) 16631501.131289305624138998115419201. C293 M (62L,74M) 18353.156129641.43944724736733414934459601. C287 2298L (2,766M) 2593247694731387242657.148540834333376678799373.P187 M (6,766L) 20895197788410280731804361141. C202 2302L 78960215773801.1739229066659377.14315531938788851695592513. C293 M (2) 36833.58727643349.1332175582691632116991109.P307 2306L 152197.67796401.487690428661.375990376657230739677009027023959553.C287 M (2) 109361035361.1083060417437.1434915902261.8556491520780190213657. .6313928863515514474051949065037.C259 2310L (2,10L,14M,22L,30M,42L,66M,70L,110M,154L,210M,330L,462M,770M) 407861310781.3276541722830542321. .2359740183446742670670667665744434142926705478881.P67 M (6,10M,14L,22M,30L,42M,66L,70M,110L,154M,210L,330M,462L,770L) 4621. .46491061.1701142565107331378341.996393112075334929736912485201.P82 2314L (2,26L,178M) 9257.P315 M (26M,178L) 217517.14647621. C306 2318L (38M,122M) 27817.679697869.4375877471939948309.344099814953387082089. .39099499295517164340521270869.C244 M (2,38L,122L) 4637.152989.580881529.1684427935189. C296 2322L (6,18L,54M,86M,258L,774M) 95851347301.37209645369951841. .6496073174630179782608508433.P173 M (2,18M,54L,86L,258M,774L) 595788049.10635930289. .201733784510995734472837.P186 2326L (2) 37217.37453253.1415424616664524411792669. .157705304785160725584866573.C287 M 3402398369.12167709806945144034936348279437.P310 2330L (2,10L,466M) 15583496780908814321. C261 M (10M,466L) 511966974989795194817109952829201. .8565602449358800368653873845874585921.C210 2334L (6,778M) 2319997.2973517.373755179958625706510646037. C194 M (2,778L) C235 2338L (14L,334L) 1122241.12586300846981.21713309717806393531167754789. C253 M (2,14M,334M) 14029.28057.254678341.P284 2342L (2) 13152673.2384970647060589977.P327 M C353 2346L (2,34M,46M,102L,138L,782M) 84457.1468398937.744513968035314938427361.C174 M (6,34L,46L,102M,138M,782L) 416806406641. .293138785158765167527809171241.P172 2350L (10M,50L,94L,470M) 263201.347801.2431220465777752225890601. .283401900451417872053764801.6911642791217739195898769605801.P185 M (2,10L,50M,94M,470L) 15012093905101.5216373323605901. C248 2354L (22M,214M) 103577. C314 M (2,22L,214L) 409597.5134243489.2696763541312061983157421198040561. C271 2358L (2,18M,262L,786M) 9433.3051253.78997717. C217 M (6,18L,262M,786L) 80173. C231 2362L (2) 8071501966620134876289473357. C327 M 1369961.9178733.7493076529.74682436939657249341097.P310 2366L (14L,26M,182M,338L) 81058592161.6749423878264140893.P253 M (2,14M,26L,182L,338M) 14197.94190461.1591950268614161.P255 2370L (6,10M,30L,158L,474M,790M) 310358259241. C177 M (2,10L,30M,158M,474L,790L) 2678101. .3655416608472669202278533979576601.C148 2374L (2) 9497.151937.19078157209.18049600319059487020771408069. C309 M 383215829.1401980222664869.P334 2378L (2,58L,82M) 71341.989249.19372762237.952283431069. C305 M (58M,82L) 409482089.15666418332748295461.19162921824083567371081. .59678323107084643519889387415017.338256594766563257848839493358293.P223 2382L (6,794M) 986149.407144053973843038498648693671401041. C197 M (2,794L) 161977.2282227514761573. C219 2386L 55665356141.6192864263277076981.19276031365740866426115587917. C302 M (2) 293731580424649.1624203343961766495413. .1412810444145553567161915193.P296 2390L (2,10L,478M) 19121.33461.219881. C273 M (10M,478L) 25864061833661.43833713434081. C260 2394L (2,14M,18M,38L,42L,114M,126M,266L,342L,798M) 4789. .5180922000084027651331204969715053.P158 M (6,14L,18L,38M,42M,114L,126L,266M,342M,798L) 1140784093. C186 2398L (22M,218M) 23981.3995157450045997881205181480047421.P287 M (2,22L,218L) C326 2^{2h}+1=L.M, L=2^h-2^k+1, M=2^h+2^k+1, h=2k-1. Table 2+(4k) Factorizations of 2^n+1, n=4k, n<=1200 n Prime Factors 4 17 8 257 12 (4) 241 16 65537 20 (4) 61681 24 (8) 97.673 28 (4) 15790321 32 641.6700417 36 (4,12) 433.38737 40 (8) 4278255361 44 (4) 353.2931542417 48 (16) 193.22253377 52 (4) 858001.308761441 56 (8) 5153.54410972897 60 (4,12,20) 4562284561 64 274177.67280421310721 68 (4) 17*.354689.2879347902817 72 (8,24) 577.487824887233 76 (4) 1217.148961.24517014940753 80 (16) 414721.44479210368001 84 (4,12,28) 3361.88959882481 88 (8) 229153.119782433.43872038849 92 (4) 291280009243618888211558641 96 (32) 18446744069414584321 100 (4,20) 401.340801.2787601.3173389601 104 (8) 78919881726271091143763623681 108 (4,12,36) 33975937.138991501037953 112 (16) 449.2689.183076097.358429848460993 116 (4) 59393.82280195167144119832390568177 120 (8,24,40) 394783681.46908728641 124 (4) 290657.3770202641.1141629180401976895873 128 59649589127497217.5704689200685129054721 132 (4,12,44) 7393.1761345169.98618273953 136 (8) 383521.2368179743873.373200722470799764577 140 (4,20,28) 84179842077657862011867889681 144 (16,48) 1153.6337.38941695937.278452876033 148 (4) 20988936657440586486151264256610222593863921 152 (8) 27361.69394460463940481.11699557817717358904481 156 (4,12,52) 84159375948762099254554456081 160 (32) 3602561.94455684953484563055991838558081 164 (4) 13121.8562191377.12243864122465612155106392056552353 168 (8,24,56) 2017.25629623713.1538595959564161 172 (4) 3855260977.64082150767423457.1425343275103126327372769 176 (16) 5304641.275509565477848842604777623828011666349761 180 (4,12,20,36,60) 168692292721.469775495062434961 184 (8) 43717618369.549675408461419937.3970299567472902879791777 188 (4) 1198107457.23592342593.4501946625921233.181352306852476069537 192 (64) 769.442499826945303593556473164314770689 196 (4,28) 7057.273617.1007441.375327457.1405628248417.364565561997841 200 (8,40) 1601.25601.82471201.432363203127002885506543172618401 204 (4,12,68) 8161.40932193.1467129352609.737539985835313 208 (16) 928513.18558466369.23877647873.21316654212673.715668470267111297 212 (4) 1692645313.10920513604018498900801.20946001591429012199281424246257 216 (8,24,72) 209924353.4261383649.24929060818265360451708193 220 (4,20,44) 109121.148721.3404676001.11035465708081.2546717317681681 224 (32) 167773885276849215533569.37414057161322375957408148834323969 228 (4,12,76) 90289.9036489073.29034057164920993379000074993 232 (8) 929.5569.8353.39594977.P50 236 (4) 1889.11329.84961.765373489.P49 240 (16,48,80) 23041.P35 244 (4) 977.37831175201.4889940029309876547089.P37 248 (8) 8929.P69 252 (4,12,28,36,84) 1009.21169.2627857.269389009.1475204679190128571777 256 1238926361552897.P62 260 (4,20,52) 42641.5746001.2400573761.65427463921.P27 264 (8,24,88) 16875081675650881.P32 268 (4) 75041.333808138537249.P61 272 (16) 5441.335631827046798245410603730138717057.P38 276 (4,12,92) 5770338946481798744593.P32 280 (8,40,56) 4481.557761.736961.P43 284 (4) 2273.1433633.P75 288 (32,96) 3457.816769.1562985901350085709953.P28 292 (4) 19602880710043505617.P68 296 (8) 80513.P82 300 (4,12,20,60,100) P49 304 (16) 7798338113.179781388993.84885296460737.643966863870017. .27362254540091201.237157827243967596481 308 (4,28,44) 13553.74153335873.P58 312 (8,24,104) 4993.94849.P50 316 (4) 504337.994769.P83 320 (64) 286721.446960641.96645260801.3442404051886487041.P34 324 (4,12,36,108) 1297.3889.30433969.1164777409.3718266498433. .134921168163073.1174029487714513 328 (8) 12239719573537.18093927039368350337.25394524415842506913.P45 332 (4) 11953.14767689550320172808742174828062347720350769.P52 336 (16,48,112) 47886721.P51 340 (4,20,68) 1361.12717361.1392971637361.8088220746627020943841.P33 344 (8) 4129.P98 348 (4,12,116) 82129.10389476529713761.59372021171164475019217.P24 352 (32) 1409.1258753.441995541378330835457.P67 356 (4) P106 360 (8,24,40,72,120) 8369281.P51 364 (4,28,52) 593914915675537.P72 368 (16) 76392570609857.1335570346574631363954390476479681.P59 372 (4,12,124) 1489.29761.22415398357688737.P49 376 (8) 3308801.3853249.487073399939357470433. .163875530636702837695009.2673989784183378728255297.P30 380 (4,20,76) 3435950210316335724157758000789490561.P51 384 (128) 349621839326921795694385454593.P48 388 (4) 25507121.P109 392 (8,56) 3137.50177.101921.258721.P83 396 (4,12,36,44,132) 311712063697.P61 400 (16,80) 3399426377632056001.4850484222084371979240001.P54 404 (4) 4126631533969610752526181761.P93 408 (8,24,136) P78 412 (4) 454849.667441.40151873.52317884766401.142500609730433.P76 416 (32) 4940417.11342687617.P99 420 (4,12,20,28,60,84,140) 127681.1130641.755667361.P38 424 (8) 1697.P122 428 (4) 4209809.13012913.992005069953996722026755979686303668059315249.P69 432 (16,48,144) 68016300334849.P73 436 (4) 598193.35695338233523972669330604417. .576694829762330794568961139476826913.P60 440 (8,40,88) 47521.89119361.127886114126296744221796660380215073025601.P43 444 (4,12,148) 92353.126097.532801.854257.85337232196804809313.P46 448 (64) 1489153.P110 452 (4) 9041.30500013280577.P118 456 (8,24,152) 1459574594862075553.320507768196690588004609.P46 460 (4,20,92) 254697295909573204954870539927521.P74 464 (16) 748264961.2245984577.239686663718401.15929619591127520827829953. .6033312171721035031651315652130497.P44 468 (4,12,36,52,156) 1873.6440452782193.623293182848475361.P53 472 (8) 25342605037666235678081.P118 476 (4,28,68) 94994369.1580019259393.115846651946400929. .2488196881582734135904733409191377.P45 480 (32,96,160) 26881.4855681.610548481.137603804161.P47 484 (4,44) 209089.33186913.1251287137. .38608979869428210686559330362638245355335498797441.P61 488 (8) 1035817877926014488587133818491976759389034764353.P97 492 (4,12,164) 62966161.P89 496 (16) 5953.251969.19301855478655894221313.32206359010364528536290817. .15624307475317816130204755452289007981717441.P45 500 (4,20,100) 4001.1074001.2020001.22624001.1481124532001.P85 504 (8,24,56,72,168) 34273.P83 508 (4) 3108961.17664039857.357319966758824298104849. .3284305317126808646829056321.78829341974215087229120114369.P55 512 2424833.7455602825647884208337395736200454918783366342657.P99 516 (4,12,172) 328177.359137.52547670996812050561. .7277473036504760410488618498577.P40 520 (8,40,104) 2081.19868746561.3377549010888001.7580827241843270677601.P65 524 (4) 1271332666556177.36441674155824796521521. .88628235147538969385874281472055436801.P81 528 (16,48,176) 1632064897.190507963147393. .44250674269198344200898981420091393.P39 532 (4,28,76) 1692116131441.139065006256539545729.P98 536 (8) 4289.311532723090035002320027134588551176448471666435989092897.P99 540 (4,12,20,36,60,108,180) 2161.21601.201519653761.1117180440577441.P53 544 (32) 15233.143617.443069456129.P134 548 (4) 38226289.15164972751718165538717288739219937057169.P116 552 (8,24,184) 267457249.P98 556 (4) 6673.77764617112817456421627629713. .1716319040365034397790860195913303021663915471096474850983729.P74 560 (16,80,112) 16824641.86800001.40396092614384641. .40809065233184155116161.P62 564 (4,12,188) 201777278450257.4409486883238989864703786561. .38573092257178550307394862497.P41 568 (8) 14254355329.80377573236449.13425464222423304875744449. .11091113376655556595890990679482099679181989410614081.P68 572 (4,44,52) 145143857.311195251370951377. .1614501783881444871695814328568586673.P83 576 (64,192) 17047297.628582818817.P97 580 (4,20,116) 6961.9281.167859997042321.P113 584 (8) 32871186029052837857.79778881726281213651073.P131 588 (4,12,28,84,196) 84673.265549217634074770386573489863592827112366481.P52 592 (16) 31474859175390153735107856059776876864094488913562623409\ 377402922304455233.P100 596 (4) P179 600 (8,24,40,120,200) 4801.55201.P88 604 (4) 2417.4363297.730685377.775168188161.P150 608 (32) 14593.671233.620066693671553. .72957037607516225290419063617993856505649915307620690006389889.P87 612 (4,12,36,68,204) P116 616 (8,56,88) 29569.110881.P135 620 (4,20,124) 6338840521320763912823441. .8972288213208726237756413079825557066213015494366305516001.P62 624 (16,48,208) 792584833.9155841480185089.P91 628 (4) 7537.118528721.262400181553.992000324534793042722401. .20605715069815219132625364745038097331729. .277433242225210532955711783957443819730099281.P56 632 (8) 286297736737. C177 636 (4,12,212) 12721.239372593.208306541869009.971476396313002897.P81 640 (128) 3288416281349499632641.7771646317471635593256655841281.P102 644 (4,28,92) 53632321.508294185549580458441687901500833. .187348880910146760908202953046841356170561257966417.P69 648 (8,24,72,216) 10369.259201.1824045366145909775041. .524833094849624730914401.P76 652 (4) 2609.10433.1322257.28322881.P175 656 (16) 7873.47402561.591100350038949953.1668576469005068046209. .506060190832207779694850270816882633281.P104 660 (4,12,20,44,60,132,220) 14736481.514210163281. .649817602852289358605542163521.P48 664 (8) 3508428556083287152033.P176 668 (4) 482851777.670297921.375283446486344365461807838534613233.P147 672 (32,96,224) 494968321.663239809. .2925384400770993343049563645260155764299463512577.P50 676 (4,52) 210913.47925697.455986337.178077806451169.P152 680 (8,40,136) 496304801.10008321601.33910825580641. .10146032011084172688350401.18741457027056199460701768016571521.P63 684 (4,12,36,76,228) 12407761.1953842221288628908086845073520488081169.P84 688 (16) 2753.1755145793.18090206003620308180353. .3374493964203314716755629762689. .77411329907915702977897669886203158137376728020417.P87 692 (4) P208 696 (8,24,232) 75169.1185335329.2175937261441.3945720769057. .43420756732422994369.247716071005295731527406385377.P47 700 (4,20,28,100,140) 2801.P142 704 (64) 60299259845689822028046342401. .3210843755324367119258027752661239735297.P125 708 (4,12,236) 95646885844433203176775508160481.P108 712 (8) 290497.59170049.9497407873.1334056289569. .25222813432549907120203219752470337287201.P137 716 (4) 94513.10240246321.6249618890312649605712432659622854257. C163 720 (16,48,80,144,240) 37441.170251201.322029272318997936286081.P80 724 (4) 2897.304081.558786628009681.148643100302189793374401. .3289754668487801751212109418730038529.P134 728 (8,56,104) 145601.9828001.32038310825249.P148 732 (4,12,244) P145 736 (32) 3689800577.6699561451777.428895600365702401. C172 740 (4,20,148) 174463386657191516033932614401.P145 744 (8,24,248) 91556187016478788158721. .2295529738871686782981597056268590225067747577438438859809.P65 748 (4,44,68) 738395681.16998871173904049. .199431288499235121583168837778864679060668081.P124 752 (16) 4087873.4810716907835700161.P197 756 (4,12,28,36,84,108,252) P131 760 (8,40,152) 3041.477822284525893121. C153 764 (4) 827467009. C220 768 (256) 212780015855109121.2220842644284984664160257. .1796602923899342630768062019504577056782884736988571649.P59 772 (4) 43464340002838801. C215 776 (8) 782209.372454540993.2125457487809.20468009784290989308737. C180 780 (4,12,20,52,60,156,260) 1928161. .166668825096179161138307580471434399036535876481.P63 784 (16,112) 689921.66308056470365249.P180 788 (4) 72497.3050841968833. C219 792 (8,24,72,88,264) 3169.3665377.12925441.52386049.P120 796 (4) 8214796852906477415899530941807101361.P202 800 (32,160) P193 804 (4,12,268) 209898673.6925799047681.29493338799546784993. .133304540580175280319733184641.P90 808 (8) 203617.P236 812 (4,28,116) 562943995510177.15902347075274017. .116248663016701150509115828530608561.P137 816 (16,48,272) 959617.597149752187286607489.47192818771332809681089. .48734995441023943825153659548266541432641.P65 820 (4,20,164) 141041.11109333761.210085224303959163308751601. C152 824 (8) 19777.88993. C237 828 (4,12,36,92,276) 1523521.257952400029937.P139 832 (64) 3329. C228 836 (4,44,76) 2368822395648721.3040124117151617. .1128504950062383934670257.C162 840 (8,24,40,56,120,168,280) 13441.4841172001.1586308510081.P90 844 (4) 91185761.P245 848 (16) 528209783809.3408818505565834978224383921527937.P206 852 (4,12,284) 13633.31141397544886408722636686759644216932367969.P121 856 (8) 1489441.229634869879668984791701633. C223 860 (4,20,172) 557281. C197 864 (32,96,288) 1718990209.8148919324033. .672915391135935402269916482777538049.P116 868 (4,28,124) 334853569.71153008417.15174698834406721.922626543715132033. .1042949211954459511633.P143 872 (8) 17547835073985096343806660481.P232 876 (4,12,292) 45553.52561.241378644784282665724224215269676274193.P126 880 (16,80,176) 32655041.374871146580481.36589369917525430721. .212669637382198127520411474271156481.P116 884 (4,52,68) 17681.572833.3327377.5882010302757468387457. .507503808182829478517537.1521590246367016260256977648481. .9490550620859983699756004482528532989220017. .459988434780718651547146575150088880586568119521.P49 888 (8,24,296) 1079809.1174047124321. .129887637532703885175569346500164339384596481.P112 892 (4) 267601.1391521.1345517777.P247 896 (128) 10753.48919385089.39257233394241687553. .328516339886958171419482857961643272193. .12914340854285079433782775726161803964147713. .77338582801985556033595814340666648061420033.P72 900 (4,12,20,36,60,100,180,300) 5807380901690048305970962748462547129404401.P102 904 (8) 3617.65089. C262 908 (4) 83537. C268 912 (16,48,304) 32833.299137.174535138510980012221761. .107464447084600919847454485663361.P109 916 (4) 24060283912401409. C259 920 (8,40,184) 18401.66083546765982085951180190942752889927681.P167 924 (4,12,28,44,84,132,308) 3697.1027489.97374817.39522602650168177.P111 928 (32) 189546985765489533095169829108497477761. .4971141705173876156149290559555016352907777.C189 932 (4) 74561.85458417577408481. C258 936 (8,24,72,104,312) 26391457.54573491387218500862753537. .174989678972338341728544129375449953.P105 940 (4,20,188) 13885681.56287943657879761.P198 944 (16) 33803203708913089579238660220728641.P245 948 (4,12,316) 3793.2707489.P178 952 (8,56,136) P232 956 (4) 765459043457.8806289643641483412983387861556412577. C238 960 (64,192,320) 49921.P150 964 (4) 1602657713. C280 968 (8,88) 30977.2555521.204452543956321.5588918964965108257. .3254976976165960099872801486011429794721.P182 972 (4,12,36,108,324) 26232337.13655624113. C178 976 (16) 361526017.21251836487537653646842236161.P253 980 (4,20,28,140,196) 7841.35281.141121.4653041.60893281.4387897103521.C162 984 (8,24,328) 349107457.628217089. .30220180022953160453457856387777914721.C138 988 (4,52,76) 189697.167659649.1482371489.6450973392449.9931868988289. C212 992 (32) 5201080300033.3085397990461441.53497190411184131713. .243889001786361258243254488269457409.P206 996 (4,12,332) P198 1000 (8,40,200) 76001.42144001.293543676001. C217 1004 (4) P302 1008 (16,48,112,144,336) 423319681.494077391563970390335488001. .7201935329692363728844274296784241409. .1006545610655423007817780018765739801419395841.P57 1012 (4,44,92) 14405614244209.924278616131729. .3693169819477873192220694097.C210 1016 (8) 131101681409.53428165972513.8431309118401633.581367694924545281. .313033168856062878953819009.P219 1020 (4,12,20,60,68,204,340) 171664686650370481.1230412270786066204321.P116 1024 45592577.6487031809.4659775785220018543264560743076778192897.P252 1028 (4) 2685107860437307121.266473139971248960398417. .39268438158946581131254913.C241 1032 (8,24,344) 242193739165634585377.702389334730574219713. .13298428572991424840707017555082369. .3662668785050561460441277306761003321502356238369.P79 1036 (4,28,148) 136753. C255 1040 (16,80,208) 201219077319973441.1493088790381629762730439505281. C184 1044 (4,12,36,116,348) 11514589201.10094533349991037489. .337138190889530707009.C153 1048 (8) 1211489.45529313.454261889.410515107056935291714767361. C265 1052 (4) 22625271329336833. C300 1056 (32,96,352) 155852929.15747624837121.46714408868623938817. .3046044023647117265076766795424257.P119 1060 (4,20,212) 4241.22625755121.378827137612775441. .23678936375488328669921.P197 1064 (8,56,152) 3404801.35868448673.477170373761089.7802057668861532450977. .1053871639906983063115212651361.4708253967270778823533486411429633.C143 1068 (4,12,356) C212 1072 (16) 107201.5028065709856661529105121236692752636100161. C271 1076 (4) 4037153.4326200033.707374699665617.208611133232063053649. .10342980458599601976190587017511281.C238 1080 (8,24,40,72,120,216,360) 6281281.148759201.4518776161. .30263419164953868175425499201.P121 1084 (4) 4337.13009. C318 1088 (64) 544001.76138241. C295 1092 (4,12,28,52,84,156,364) 26209.279553.404284148686608554495041. .1580204575585229261365153. .69864226063509680379988083391904586415696439739773112049.P60 1096 (8) 457024161409.63074817527233.1188755858465841569.P284 1100 (4,20,44,100,220) 567601.277173601.333742931196401. C213 1104 (16,48,368) 26497. C208 1108 (4) 13297.476041121.2550041661553. .7910906581519939367772674324430352577.C271 1112 (8) 934309676929.P321 1116 (4,12,36,124,372) 1093681.P211 1120 (32,160,224) 8539067456641.101750737670401.1146946484544001. .5344315494149074932607669859871361.C156 1124 (4) 205107521.1496800817300278753. C311 1128 (8,24,376) 1078369.7341898433044801. C200 1132 (4) 275814838289.362073730366785443780868881.P302 1136 (16) C338 1140 (4,12,20,60,76,228,380) 4561.P170 1144 (8,88,104) 25744577.377140193. C274 1148 (4,28,164) 30645407522290070293105505369518259537.P252 1152 (128,384) 18433.27733723987969.87706468640521797294901519524699649.C179 1156 (4,68) 17*.41617.295937.83736716905921.31148444724976529. .2428691128313288513.P268 1160 (8,40,232) 977403570406117601.841464143582829714489281. .57281536092725157009193935521.P200 1164 (4,12,388) 5106360913. C222 1168 (16) 4673.1137948235396559809. C326 1172 (4) 9377.1345457. C342 1176 (8,24,56,168,392) 3040410389842561.5091542821206332688289. C166 1180 (4,20,236) 89681.141601.1250801.13083841.106827761. C249 1184 (32) 9473.1202741777537.414581855009107748596797028667339521.P296 1188 (4,12,36,44,108,132,396) 427681.59008134786334273. C195 1192 (8) 255373980342366346612993.P334 1196 (4,52,92) 38273.14536633697.36919357139916161. .14755410932634657950998395089.1757744807679263833464910204577. .122255024596887310384016956082161.C197 1200 (16,48,80,240,400) 9601.57601.17963653814841601.P168 Table 3- Factorizations of 3^n-1, n odd, n<540 n Prime Factors 1 2 3 (1) 13 5 (1) 11.11 7 (1) 1093 9 (1,3) 757 11 (1) 23.3851 13 (1) 797161 15 (1,3,5) 4561 17 (1) 1871.34511 19 (1) 1597.363889 21 (1,3,7) 368089 23 (1) 47.1001523179 25 (1,5) 8951.391151 27 (1,3,9) 109.433.8209 29 (1) 59.28537.20381027 31 (1) 683.102673.4404047 33 (1,3,11) 2413941289 35 (1,5,7) 71.2664097031 37 (1) 13097927.17189128703 39 (1,3,13) 13*.313.6553.7333 41 (1) 83.2526913.86950696619 43 (1) 431.380808546861411923 45 (1,3,5,9,15) 181.1621.927001 47 (1) 1223.21997.5112661.96656723 49 (1,7) 491.4019.8233.51157.131713 51 (1,3,17) 12853.99810171997 53 (1) 107.24169.3747607031112307667 55 (1,5,11) 11*.1321.560088668384411 57 (1,3,19) 229.248749.1824179209 59 (1) 14425532687.489769993189671059 61 (1) 603901.105293313660391861035901 63 (1,3,7,9,21) 144542918285300809 65 (1,5,13) 131.3701101.110133112994711 67 (1) 221101.441019876741.475384700124973 69 (1,3,23) 277.2461243576713869557 71 (1) 3754733257489862401973357979128773 73 (1) 11243.20149.15768033143.9460375336977361 75 (1,3,5,15,25) 601.9601.2098303812601 77 (1,7,11) 51457561.7151459701.76831835389 79 (1) 432853009.392038110671.145171177264407947 81 (1,3,9,27) 3889.1190701.12557612956332313 83 (1) 167.12119.1036745531.950996059627210897943351 85 (1,5,17) 2663568851051.862970652262943171 87 (1,3,29) 74821.32234893.150224123975857 89 (1) 179.1611479891519807.5042939439565996049162197 91 (1,7,13) 4011586307.3745603812007166116831643 93 (1,3,31) 1117.26273701844015319144827917 95 (1,5,19) 191.78958087694609321439660131899631 97 (1) 76631.2549755542947.48845962828028421155731228333 99 (1,3,9,11,33) 3186217.12812432238302009985937 101 (1) 33034273.465092326319.50316775668019759306202964023 103 (1) 6957596529882152968992225251835887181478451547013 105 (1,3,5,7,15,21,35) 421.6301.1616161.26751945361 107 (1) 50077.229837.48965028505045123993421250406516036571557 109 (1) 1091.521402591.3499901929.239789806103.10624346875389299603 111 (1,3,37) 18702169.119779213.6962353413269964253 113 (1) 227.1583.2172539.526256453012063980796131127321354599535039 115 (1,5,23) 1975931.6273542442241.52370346649565455417091 117 (1,3,9,13,39) 4162861.1846794457.2821964307371847613 119 (1,7,17) 239.44626806191326911791.397881837642577477902049 121 (1,11) 11617.3981923614021.657890411545272648205502849240259841 123 (1,3,41) 51169.1999827817517387044561568810795329 125 (1,5,25) 251.358291751.14781691751.391632555001.989947158849251 127 (1) 5843.681229.21520151.76082653.301515315752300874236564235591357673 129 (1,3,43) 4129.2199072289.912851565662857110894244969 131 (1) 263.605199588591144003100881306574406851660288427740394885828171 133 (1,7,19) 8757948941961838067.257513776243156826379279929309507 135 (1,3,5,9,15,27,45) 541.53825041.773618132427345151923061 137 (1) 4933.217629707.108081809773839995188256800499141543684393035450350551 139 (1) 1669.5430731.P57 141 (1,3,47) 161969595577.2031161085853.165301473942399079669 143 (1,11,13) P58 145 (1,5,29) P54 147 (1,3,7,21,49) 47041.P36 149 (1) 7451.177941761.P59 151 (1) 1511.6263783.64745079361.P51 153 (1,3,9,17,51) 6213394261.35106034213.P26 155 (1,5,31) 311.3586225081.P46 157 (1) 9421.3381925092493.9891109125337566719.P40 159 (1,3,53) 712550912937217.P35 161 (1,7,23) P63 163 (1) 5227348213873.8882811705390167.P49 165 (1,3,5,11,15,33,55) 50821.P34 167 (1) 58451.88177.1767863.10063060897082377.P48 169 (1,13) 2029.163264150141.P60 171 (1,3,9,19,57) 119701.P47 173 (1) 347.762239.2125048865543.P62 175 (1,5,7,25,35) 109201.1430128198787051.P38 177 (1,3,59) 709.2224898159852613649.P34 179 (1) 359.56207.100957.19510643.291066066130451.6779963644378513811.P33 181 (1) 90863.890159.P76 183 (1,3,61) 733.97806913.2421854958301.P34 185 (1,5,37) 2221.17761.35521.146891.228082801.49804972211. .87841814842081.1654235911196704741 187 (1,11,17) 6359.1272753542934479.3411926755457243.P42 189 (1,3,7,9,21,27,63) 49888641454623789553.P32 191 (1) 383.311713.9593931911.P73 193 (1) 6563.29723.2346066378779.218246094772601642186973037.P45 195 (1,3,5,13,15,39,65) 2341.39838501.P35 197 (1) 9851.741019334164502879.11472574961994477441469621.P47 199 (1) 1360648969.293366430131930353811221418233.P57 201 (1,3,67) 1089421.P57 203 (1,7,29) 2843.735673.P71 205 (1,5,41) 6971.31981.P68 207 (1,3,9,23,69) 829.1657.4969.P54 209 (1,11,19) 419.2927.99381983898121.340838185560681043030809047.P40 211 (1) 2111.962188370639.54046656969013.5676687374958905209. .1695949409060064182746451.P29 213 (1,3,71) 5113.22716867932413.115264393627813.3613512804721129. .89665588664737776553 215 (1,5,43) 8477881.14491125481091320910774351.P48 217 (1,7,31) 20399.24040333283.20545698698839917414079969.P46 219 (1,3,73) 135781.P64 221 (1,13,17) 443.P89 223 (1) 54473097204950819531444809.P81 225 (1,3,5,9,15,25,45,75) 116101.875701.286870274711101. .515009259868501.119634969443826601 227 (1) 19907051929.86695423725589885803695742296342497463.P60 229 (1) 8047106008391.32356561399076305309.284663996630519253661. .634538541879036040523.P36 231 (1,3,7,11,21,33,77) 3697.73155606217.P43 233 (1) 467.27599172691870182517.6354979252162209284471. .38247482016765032274959.P45 235 (1,5,47) 5171.11321831.1287586151.30168205545535224185322498361.P40 237 (1,3,79) 37520893.52802131282482966001751707837.P38 239 (1) 479.17209.43301964055635533333945745533106128044213.P67 241 (1) 553788718707122198751861425724478919.P79 243 (1,3,9,27,81) 70957.6627097.21835473162448454819220238921.P38 245 (1,5,7,35,49) 32341.P76 247 (1,13,19) 14327.50427403417.85336889516918333646696709.P63 249 (1,3,83) 35882730354181.P65 251 (1) 503.5894996162509148852365257446042626007.P80 253 (1,11,23) 23*.38636905168680714294388463.P78 255 (1,3,5,15,17,51,85) P62 257 (1) 120277.1329772662933524112502310453951741137.P82 259 (1,7,37) 2591.18131.P96 261 (1,3,9,29,87) P81 263 (1) 53653.78901.2750510656513.65397307474141.153572905037740933. .352436749324038579121.P52 265 (1,5,53) 3181.18474777940736174884324451.3449313707942322494318140511.P43 267 (1,3,89) 850666273.2270061722000879968839976583683542421.P39 269 (1) 10223.262007.116075653.76305384036997.299470647963251.P83 271 (1) 3253.8916443.490543245624181.2709600825365281117.P86 273 (1,3,7,13,21,39,91) 30577.1636991658121.2148920356182437964673.P31 275 (1,5,11,25,55) 121083372541491664042201.P73 277 (1) 15801743.478803193369.P113 279 (1,3,9,31,93) P86 281 (1) 563.3373.422063.434989.1000081249.38012519036699. .124205327610431.543615007915184215523.2397212236344676495763.P38 283 (1) 133227911.1830824353.306487563493.1257602943398454563.P88 285 (1,3,5,15,19,57,95) 5731756981.P60 287 (1,7,41) P115 289 (1,17) 44507.1088953.P120 291 (1,3,97) 189733.1693621.80640757.184812684901540537.P55 293 (1) 587.64911612051881874971.P117 295 (1,5,59) 739861.311834125441.1243704975397142761851514391. .15800757982738113728531939755751.P35 297 (1,3,9,11,27,33,99) 1182737161.7899901813.370231459035769.P53 299 (1,13,23) 599.10997221.2886381073947332989.8661965714512154562493.P76 301 (1,7,43) 8127001.921928537909.31575110690775101163983809. .2954696283347370339434959009.P49 303 (1,3,101) 1213.464114346100971670261030354878981449019613.P51 305 (1,5,61) 65881.4919054377091. .46229214937048975901175732207117334435811.P57 307 (1) 10610542242923144869.1209358403350153553775181.P104 309 (1,3,103) 1237.16069.P90 311 (1) 3733.12460588823.873069502041694941443. .2241207330424850668586082361185081412667449.P72 313 (1) 2370037.3759897752153653302941126019779. .2714675534408576046409316982151068303918417599.P67 315 (1,3,5,7,9,15,21,35,45,63,105) 1571221.P63 317 (1) 3493595928049.199057440042898163364095413.P113 319 (1,11,29) 3191.113164935467.26425387421490471188793734763177943613329.P79 321 (1,3,107) 3853.6421.1276775957917.P82 323 (1,17,19) 647.1600789.39039719.29134285181591.P108 325 (1,5,13,25,65) 217520261488056211634951. .27612401161496267925537524217847751.P57 327 (1,3,109) 122953.1340701.55471745029. .714322353831283890903559265735120995717.P43 329 (1,7,47) 659.16451.94041956807.P114 331 (1) 1581832451.16312845121. .530654464353667468092169451245888744365152829791.P91 333 (1,3,9,37,111) 1179099721.2628354173876461837.P76 335 (1,5,67) 2791110259168381.P111 337 (1) 8089.338861091937.736092762241.P134 339 (1,3,113) 51017244973.283274887324515433.P79 341 (1,11,31) 4093.9484546040170844481070590623.P112 343 (1,7,49) 24697.385540919.4551588049.8465728310029191083. .23451446896560788630183.32312015265609073916797.P54 345 (1,3,5,15,23,69,115) 1381.9661.31741.6784081.76675561.P58 347 (1) 291481.1150057146229.185498348145073.328003153456707623. .20912010800475074747.33844448484642846054095202148071217.P63 349 (1) 9404285088998451099828915232043854179853201802165395628374\ 1193211654025280185459.P87 351 (1,3,9,13,27,39,117) 244297.503457454452889.P83 353 (1) 509027.4088777503007.P150 355 (1,5,71) 734346611.66824157595186257988571.P102 357 (1,3,7,17,21,51,119) 20001459491011594009.P73 359 (1) 719.169998846011.470920899227107034926837. .41996290825582863451929997.278252468335029499500820080150443.P76 361 (1,19) 103969.930643561.1544679802763873663. .212442076518129661950839.675873510595715629396212612371.P78 363 (1,3,11,33,121) 1453.49369.312284816501197.46007931271317089317. .1377783168921566387641.P42 365 (1,5,73) 1030031.1472874512323892527561. .154738943915325955520331463109617606098450974126281.P60 367 (1) 11665463.667804211.137673218986445617.189120585817572803. .41234466042798529583. .1511495257840070716998865694022937935039928231350493.P54 369 (1,3,9,41,123) 1767210188478589.P100 371 (1,7,53) 743.18485797607002442471500555321. .17177672994159234619140207492038707631055212708408339.P66 373 (1) 298510218291433104616283959755194459478244623487569332624\ 6633144966957389.P106 375 (1,3,5,15,25,75,125) 8788416011598893375808561717543001280896024501.P50 377 (1,13,29) 4338169506098819.1726610752347421021849.P124 379 (1) 210917324869.1518049814692403. C155 381 (1,3,127) 597409.2896724388952980361.P96 383 (1) 23747.2835733.263172186419.428039526143.999607767985979. .1085363716480624115399141696533.P104 385 (1,5,7,11,35,55,77) 225611.868561. .10758904556355084920587039558086313081.P67 387 (1,3,9,43,129) 308842594561.269123363760531549673.P89 389 (1) 51349.19404514058063. C168 391 (1,17,23) 17987.94214579.2837442021361921.1136310624674027548741. .1720132331768569247939.72643760507536226775553. .947813454284697545292967550627029.P42 393 (1,3,131) 2083574227432941258356498327796750385623056105089493677.P70 395 (1,5,79) 5531.231040361073709413931057501.6434943291436769366927146921. .15726644297407162541884251721.5478828409328216056558228587181.P32 397 (1) 366829.2233523. C178 399 (1,3,7,19,21,57,133) 49279693.1068595417.89076199828580322541.P67 401 (1) 90932896832200086926891164728383761. .5865500973936060729431154988451238023.P120 403 (1,13,31) 121674645534469.14392455313096812239313539411.P130 405 (1,3,5,9,15,27,45,81,135) 155521.285121.2820618974881.P80 407 (1,11,37) 18354073.1862400449807666627.P147 409 (1) 20720759.145724851390704755159.149201935333301250525828683.P142 411 (1,3,137) 2115829.634432753.685934341. .113938829134880224954142892526477.P74 413 (1,7,59) 827.4957.48301177.366438032528092142507. .3721114359214874154231319889680078283. .37698754823547437188883025448675820051387027651.P48 415 (1,5,83) 363541.1333811.223210122334888198292034419263747875011.P107 417 (1,3,139) 43302949.2016598657.201360112381724767096677592621.P86 419 (1) 839.596113491371.2151506053058735838822709777. .654885891476141016165461375447.1593204794095231348491880857761413. .496097134087521646396618935298341361.P59 421 (1) 1206587.6804488281.129208238531.30289645235740564742379791. .4635694062476599636809044531.10722271475553804482227981559844589.P87 423 (1,3,9,47,141) 55837.57529.27115993.35675821.P108 425 (1,5,17,25,85) 49354957842491569509980274834655501. .445538977312957153485923190322961189401.P80 427 (1,7,61) 98386025627.562686760931.84404570448444086183953. .3556068841871225054499505739.P99 429 (1,3,11,13,33,39,143) 2175889.64139087689249.103304599144666396621.P75 431 (1) 863.31033. C198 433 (1) 218233.7945316512501413421855357.6152250713758461148996890901. .3336469615060863393363305195427888169.P112 435 (1,3,5,15,29,87,145) 34118036879281.221485711052594564349712441.P68 437 (1,19,23) 4400140239259780643.15627149386345831933. C151 439 (1) 32983465912566571821412548179.P181 441 (1,3,7,9,21,49,63,147) 2204277929951182849. .407888431426111186599600583446287711634101230416829.P52 443 (1) 887.298583.44457709.213177803. C187 445 (1,5,89) 477126751861.2912333801178961.P141 447 (1,3,149) 17881.P137 449 (1) 14112071.88173395548188366438189921318359. C175 451 (1,11,41) 47807.6704567.5295342260891. C167 453 (1,3,151) 2689557037.20851551949.8824691215488669109. .2210252986790978093597221.P80 455 (1,5,7,13,35,65,91) 911.386134706231.2478098909059595945200318151. .1435809872133506127696992748549282318301.P57 457 (1) 176540143789.10976741555411.790112768389761097. .44526916528666152642757247913322427.P141 459 (1,3,9,17,27,51,153) 3673.230736771829.889501314241. .11786772814775877294179029.122217754676326531200106433310349.P54 461 (1) 11987.118164568780375261. .1203473922272303966282236445337792145487543.C157 463 (1) 11113.83341.155569.1767202459333.P195 465 (1,3,5,15,31,93,155) 146941.4307761.6184582891232396881.P85 467 (1) 27836167022857.P210 469 (1,7,67) 1306456857231927329331341682365113787.P153 471 (1,3,157) 95232991961590105161615580822336892311998189163571236402837.P90 473 (1,11,43) 947.1815542308537.1261183235795048844037. .201972084490941146836006403755873.P132 475 (1,5,19,25,95) 2057701.4490080243969653901.P147 477 (1,3,9,53,159) 39365302681.954458120492216837136711901.P112 479 (1) 2017549.52133736060349.257620598280719473. .10332092185328194888766505728921146249.P154 481 (1,13,37) 709957. C201 483 (1,3,7,21,23,69,161) 696032619727190918566594730968478467309.P88 485 (1,5,97) 971.145501.22836387874896451734446934241. .163135411964857917127880147033711.P115 487 (1) 12364016389. C222 489 (1,3,163) 107581.P150 491 (1) 983.24551.844124016018569089.155447385335258570051.P189 493 (1,17,29) 135769072957854733. C197 495 (1,3,5,9,11,15,33,45,55,99,165) 35669701. .37073055770742955860149669357943581889942083408919721.P55 497 (1,7,71) 3984424151.432547838166529.1309567972706389369. .428692823469180744251.13872998573921896220953. .785010913523701739507985671014620709.P80 499 (1) 1919016277.716332093275045781.114551315779689543877. .32242867762626707702019834661.1242829528432779408196747984311772979.P126 501 (1,3,167) 218437.4769521.777324624268955461.12015367658187607573.P110 503 (1) 7043.12073.30311006351.41692265961952424506975231211.P193 505 (1,5,101) 205031.3732938536661701. .276878587446880592989075966008807841.P135 507 (1,3,13,39,169) 13*.2624233.580460684077.13956160423453. .5242148588473376340853.P95 509 (1) 1019.7127.54973.97729.14495303.324927277. .59561824373572167761652488341. .1408323592065265621229603282020508687.P146 511 (1,7,73) 16347913.2429424817.2126913191482456609.P172 513 (1,3,9,19,27,57,171) P155 515 (1,5,103) 1031.13904017381. C182 517 (1,11,47) 18121754584561.11564421035953127. .195823481748025157463422904654781. .439353102824911497759602166124705290731.P120 519 (1,3,173) 4153.78539233.5907694552891069.P137 521 (1) 394004822498482103.1113152871547083276871904557.P204 523 (1) 8321977.4613832781. C233 525 (1,3,5,7,15,21,25,35,75,105,175) 81901.2181094346193283895070901.P86 527 (1,17,31) 592116121.60805701944219890543261. .35323611400399730994438310886415603767.C160 529 (1,23) 259211. C237 531 (1,3,9,59,177) 3030949.318413423593.52482008124253. .179197588057109824392880988379522349.P100 533 (1,13,41) 218531.13847341.1930037901921949. C202 535 (1,5,107) 5351.18191.467591.12476029871.1357991694228074281.P161 537 (1,3,179) 4297.749352523284764318713.8568932552695444750981. .475397205540953687028104590513677195842929.P82 539 (1,7,11,49,77) 20483. C197 Table 3+ Factorizations of 3^n+1, n<=540 L,M for n=6k-3<=1077 n Prime Factors 1 2.2 2 2*.5 3 (1) 7 4 2*.41 5 (1) 61 6 (2) 73 7 (1) 547 8 2*.17.193 9 (1,3) L.M L 19 M 37 10 (2) 5*.1181 11 (1) 67.661 12 (4) 6481 13 (1) 398581 14 (2) 29.16493 15 (1,5) L.M L (3) 31 M 271 16 2*.21523361 17 (1) 103.307.1021 18 (2,6) 530713 19 (1) 2851.101917 20 (4) 42521761 21 (1,7) L.M L (3) 7*.43 M 2269 22 (2) 5501.570461 23 (1) 23535794707 24 (8) 97.577.769 25 (1,5) 151.22996651 26 (2) 53.4795973261 27 (1,3,9L,9M) L.M L 19441 M 19927 28 (4) 430697.647753 29 (1) 523.6091.5385997 30 (2,6,10) 47763361 31 (1) 6883.22434744889 32 2*.926510094425921 33 (1,11) L.M L 176419 M (3) 25411 34 (2) 956353.1743831169 35 (1,5,7) 374857981681 36 (4,12) 282429005041 37 (1) 18427.107671.56737873 38 (2) 5301533.25480398173 39 (1,13) L.M L 157.10141 M (3) 79.2887 40 (8) 14401.128653413121 41 (1) 33703.270547105429567 42 (2,6,14) 2857.109688713 43 (1) 82064241848634269407 44 (4) 89.2382953.56625998353 45 (1,3,5,15L,15M) L.M L (9M) 387631 M (9L) 755551 46 (2) 12553493.70601370627701 47 (1) 16921.256057.1534179947851 48 (16) 76801.24127552321 49 (1,7) 857643277.127522693159 50 (2,10) 5*.101.394201.61070817601 51 (1,17) L.M L (3) 613.30091 M 129159847 52 (4) 2093124281.37644053098601 53 (1) 78719947.61557605176233223 54 (2,6,18) 150094634909578633 55 (1,5,11) 659671.24472341743191 56 (8) 113.19489.36214795668330833 57 (1,19) L.M L (3) 3079.53923 M 1162320517 58 (2) 12413.37945127666529000523013 59 (1) 3187.1108439448677340328268341 60 (4,12,20) 241.298801.26050081 61 (1) 367.86630432442539925437931403 62 (2) 1403808961.2860659169.9500438809 63 (1,3,7,21L,21M) L.M L (9M) 127.883.2521 M (9L) 550554229 64 2*.1716841910146256242328924544641 65 (1,5,13) 105919308797935444986721 66 (2,6,22) 13490012358249728401 67 (1) 5390821.4299412981246169975118907 68 (4) 137.6458150122561.3833564416504313 69 (1,23) L.M L 139.5107.132619 M (3) 9109.1476463 70 (2,10,14) 28596961.32839661.94373861 71 (1) 853.2131.82219.3099719989.4052490063499 72 (8,24) 1418632417.56227703611393 73 (1) 439.38488154120055537150068589763279 74 (2) 149.953861.142659759801404920771391593 75 (1,5,25) L.M L (15M) 26251.119101 M (3,15L) 2551.1530601 76 (4) 761.31769.3302353.278733912072436804273 77 (1,7,11) 56495392933101222275861053369 78 (2,6,26) 325729.271722723752757889 79 (1) 66361.327220181191.567239060331150635317 80 (16) 8194721.700984481.597747428754241 81 (1,3,9L,9M,27L,27M) L.M L 163.208657.224209 M 1297.5879415781 82 (2) 2088869.110767897.574933708017116710865237 83 (1) 499.997.2466097.813201725710097952736361977 84 (4,12,28) 337.673.1009.167329.2108826721 85 (1,5,17) 1531.224401.13271362257832586268931 86 (2) 173.470593.2641485701.55473422113.903239908009 87 (1,29) L.M L (3) 261697.37464463 M 349.142159.1383301 88 (8) 6922081.15656839738849.1363620137403810529 89 (1) 264331.1125706177.2444322641415331355533344283 90 (2,6,10,18,30) 176401.452808441334403281 91 (1,7,13) 8737.595141.2354116499281.2452788561133 92 (4) 1289.743170846305411756447828504941347481129 93 (1,31) L.M L (3) 88239050462461 M 373.541447.3058399 94 (2) 563838649753.125384283132205265785477849439329 95 (1,5,19) 39901.29574984661.25349956307509384561 96 (32) 7297.68737.96948097.70613232600577 97 (1) 459991849.503803759819.20591603926857377806745611 98 (2,14) 197.16661.251325313.426712077457.34013149495921 99 (1,3,11,33L,33M) L.M L (9L) 199.4357.337448233 M (9M) 397.378450588583 100 (4,20) 133201.18055139801.61459926512826500975801 101 (1) 379963.1017291527198723292208309354658785077827527 102 (2,6,34) 409.49637281.187668407555352123529 103 (1) 619.3661040653.1535090713229126909942383374434289901 104 (8) 1249.13729.475356961.780464337846444296785447886881 105 (1,5,7,35) L.M L (15M,21M) 24151.3369031 M (3,15L,21L) 211.1051.3454081 106 (2) 90313.609422621.1481588501.460740683381672021327601001 107 (1) 643.100153.4375617272295428356111030724847180250451293 108 (4,12,36) 2161.15121.10512289.16569793.3958044610033 109 (1) 1992772009.5933538193981.7696680097963.27866471458012723 110 (2,10,22) 177101.927319729649066047885192700193701 111 (1,37) L.M L 223.25709599.78539161 M (3) 64326272436179833 112 (16) 14561.45697.101921.643553.67765601.378369377.5685756833 113 (1) 362053.156472231.3626038130651680583578933430931295416667 114 (2,6,38) 457.2281.7753.3093009324389492947932121 115 (1,5,23) 6211.48991.4232020527831352569905247101633701 116 (4) 233.4177.277991360381003661564752468378981135693842991081 117 (1,3,13,39L,39M) L.M L (9L) 937.37441.6079786129 M (9M) 1171.2161927.43264261 118 (2) 19966781110160346782368664772328944885905284750420567849 119 (1,7,17) 7719769.1098440018152695917905622020432593239209 120 (8,24,40) 4801.13921.51383579021948491809121 121 (1,11) 727.2179.74779.256900099994436377787031292704214632407889 122 (2) 180317.262199473.39504363995133913.865923475887669700104067517 123 (1,41) L.M L (3) 40049539.130099576237 M 2337001.15606752580607 124 (4) 81516726600079249.21775844224805408923066692226998392022049 125 (1,5,25) 2251.100501.2278135721427929786778229917312351656251 126 (2,6,14,18,42) 1180369.475110761833.40226570408250073 127 (1) 22861.63247.52147471.13030796206528578864006320088875125740738871 128 2*.257.275201.138424618868737.3913786281514524929.153849834853910661121 129 (1,43) L.M L (3) 1651439941.28395735937 M 1549.27091.7822354593043 130 (2,10,26) 82669546937641.85515537811724373585467087637721 131 (1) 787.114742271896804438572098194909.881304930739946561320646289889 132 (4,12,44) 660001.11096576833.20431242370346923068097 133 (1,7,19) 11173.1084483.1256610601.295966423763788589324732476512991 134 (2) 269.1609.1877.11257.50546266229.719571227339189.P25 135 (1,3,5,9L,9M,15L,15M,45L,45M) L.M L (27M) 3511.487891.86548771 M (27L) 4591.451441.73321201 136 (8) 17*.5641553.23229617.2670091735108484737.P28 137 (1) 82093596209179.P51 138 (2,6,46) P43 139 (1) 26436515641.1113626506203380968993.P35 140 (4,20,28) 281.18481.369879560116990841.3353336738929580410561 141 (1,47) L.M L 283.93953407627827115729 M (3) 3798402051319990403467 142 (2) 3672239816477.9159751032889.P42 143 (1,11,13) 53197.P53 144 (16,48) 77826286120321.P32 145 (1,5,29) 59086051.25481953741.3159421788711031.76455796243959454561 146 (2) 293.18678646095653.86782247836514775846688349.P27 147 (1,7,49) L.M L (21M) 119471899.882757098511 M (3,21L) 7*.1471.3529.15583.200568859 148 (4) 410257.9537896093307601.31199592961514012689.P28 149 (1) 4482722618976860674653013440107317.P37 150 (2,6,10,30,50) 1201.55201.P31 151 (1) 472027.645979.135286639.P52 152 (8) P69 153 (1,3,17,51L,51M) L.M L (9M) 436357.133395235891527691 M (9L) 919.123343105382171675857 154 (2,14,22) 671352452318708161.P40 155 (1,5,31) 1861.33131555630426311.318620421994509961.121462982451478217731 156 (4,12,52) 309746737.P38 157 (1) 252457.159420524134654609.32129434337475049222622287.P27 158 (2) 317.10393819190815276250780568850989337.P38 159 (1,53) L.M L (3) 2769035095381770614187391 M 48973.395794533062864139307 160 (32) 4151768361337614527605197761.P34 161 (1,7,23) 967.1933.5468575720021.P45 162 (2,6,18,54) 82434619394313344569.P32 163 (1) 8483499631.4956470591980320134353.P46 164 (4) 41*.2297.32326369.P64 165 (1,5,11,55) L.M L (3,15L,33M) 4951.1286011.4968781621 M (15M,33L) 331.991.11123788282861 166 (2) 2591261.6956557366277.P59 167 (1) 41332144291.196098784741.P58 168 (8,24,56) 13441.P42 169 (1,13) 4057.351859.7336932438768271.P50 170 (2,10,34) 7674481.P55 171 (1,3,19,57L,57M) L.M L (9M) 25309.1676620643529235921057 M (9L) 19*.42509373931.102310358933917 172 (4) 226519873.21376165893692833.P56 173 (1) 993367.14427163.125330011023211.156026417563831897.P38 174 (2,6,58) 19437193.1388985225193.P35 175 (1,5,7,25,35) 23185675801.4260648635770037050051.P26 176 (16) 353.19009.62210098369.205188547169.P48 177 (1,59) L.M L 38926393657.363002702388730267 M (3) 76819.15743388547.1669126011067 178 (2) 1192464167514295068582330293.P57 179 (1) 3755779.47029186391731.9248363581047133.P49 180 (4,12,20,36,60) 116809201.2081711451601.P26 181 (1) 51043.715722801240612811884999961.P55 182 (2,14,26) P69 183 (1,61) L.M L 189223.6117064141.109870115206699 M (3) 279666823.64961725048119249391 184 (8) 112241.2057857.2190337.4475616001.79781171123090497.P40 185 (1,5,37) 10322251861.4183611889192231.55223513719943993551.P24 186 (2,6,62) 5853105289.1137273143641.P36 187 (1,11,17) 18177792435744585993179560027.P49 188 (4) 4513.2563193.P78 189 (1,3,7,9L,9M,21L,21M,63L,63M) L.M L (27M) P26 M (27L) 379.84673.30354157.60439117411 190 (2,10,38) 70578185345621.4975481820118441.P40 191 (1) 176349919.854888497.P74 192 (64) 280321.15687169.339601921.3167109739009.P28 193 (1) 167911.679747.7967041.32685391867.P64 194 (2) 389.1209361321548310091770485682269470852086753.P47 195 (1,5,13,65) L.M L (3,15L,39M) 54975287251.3785998525531 M (15M,39L) 419437201.56919999055921 196 (4,28) 342875768396449.P66 197 (1) 8714655511.24742960162351.49676157359100536013871955394289.P39 198 (2,6,18,22,66) 4401193897.3571691108833.P36 199 (1) 2389.5484043.P85 200 (8,40) 401.P74 201 (1,67) L.M L (3) 32563.1351123.301027886874675599533 M 275371.5931946571197.56755588835611 202 (2) 1189912513.69531972955397.96207837407260037.P56 203 (1,7,29) 398858013926743539066881263.P54 204 (4,12,68) 53958784909638588059956801.P36 205 (1,5,41) 1164811.6749930086876080531836671.P46 206 (2) 1522395676033.7625998476893.3276710054092300162911791926389341.P39 207 (1,3,23,69L,69M) L.M L (9L) 5724793.7671021268285255340377531 M (9M) P32 208 (16) 1614913.20634017.2763736726854088129.P60 209 (1,11,19) 8779.146719.227123983153149333776852194879434768181.P39 210 (2,6,10,14,30,42,70) 4201.7035101641.871383685710721.222665666643176401 211 (1) 892531.189250543.2645385196586430249915420486682565415343.P47 212 (4) 1079398849.1135214993571937.1331247175934064574966369960667813849.P40 213 (1,71) L.M L 210019.49682251.55126531.13055351529193 M (3) 12685215427.84569390002476091110121 214 (2) 582937.2827369.3096650621.481786776662041.499965737866229.P51 215 (1,5,43) P81 216 (8,24,72) 1155169.P63 217 (1,7,31) 1303.89839.174469.35258161.1023879682351. .70961158264970285776591.P31 218 (2) 2617.5233.P96 219 (1,73) L.M L 741973.P29 M (3) 877.P32 220 (4,20,44) 7481.15401.131561.P64 221 (1,13,17) 506533.278300881.P78 222 (2,6,74) 9769.4010575301861137.P50 223 (1) 19849231.249693347977.3619936401181.2784009098113351. .130559956932626998645445231983.P30 224 (32) 449.8513.31539199370561.1269624189254401.3356086147916993.P41 225 (1,3,5,15L,15M,25,75L,75M) L.M L (9L,45M) P29 M (9M,45L) 1801.16985251.697381651.1988005951 226 (2) 2713.798087896392921.P89 227 (1) 28603.31327.1533148921.28279305227149.75743328083517433389294793.P51 228 (4,12,76) 2842147681.P60 229 (1) 169003.4032176417327894814764968543.P76 230 (2,10,46) 461.5521.P78 231 (1,7,11,77) L.M L (3,21L,33M) 463.910237483.242613305580091909 M (21M,33L) 10627.1286903793030368825203123 232 (8) P107 233 (1) 1399.6991.P104 234 (2,6,18,26,78) 5589928324657.P56 235 (1,5,47) 717838945155421.1641374046359401.7061686540772491.P42 236 (4) 87793.66454972460489.79024015559441654878348076969.P64 237 (1,79) L.M L (3) 14221.2275201.P27 M P38 238 (2,14,34) 719575263747470241217.P71 239 (1) 14341.170647.42124768369936320790693.P82 240 (16,48,80) 3875067470401.P49 241 (1) 4339.281971.1837867.43195076631439.48557382169494007737217333.P60 242 (2,22) 34849.P101 243 (1,3,9L,9M,27L,27M,81L,81M) L.M L 487.59779.2051893.859270843.8638915776957163 M 572023.5062663.1319934691.116004991998176173 244 (4) 2441.123450337.740767954561.1206708060834097. .4100906420054031805880028751022497.P43 245 (1,5,7,35,49) 174931.P75 246 (2,6,82) 195817.336529.65765641.4221482364108929706493417.P34 247 (1,13,19) 8893.74154686428369.62568550770275094093451149019411003.P51 248 (8) 4002721.400317813041.P97 249 (1,83) L.M L 1993.57957241.9839624437.3511321676267937799 M (3) 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95665033.24071705219862678529. .817576445040642684875975963157408264856921.P57 807 (1,269) L.M L (3) 5191863397940689668569933101.P100 M 54877.25588357.93494549298854768677. .1667434534078422877501816329924811.P64 813 (1,271) L.M L (3) 1627.58537.2230873.8475830822135212338398067962551832652525613.P72 M 13863159773521.62014564661966845526233585639.P88 819 (1,3,7,13,21L,21M,39L,39M,91,273L,273M) L.M L (9M,63L,117M) 3018697947220411.39685911678305092747.P69 M (9L,63M,117L) 7754293.P97 825 (1,5,11,25,55,275) L.M L (15M,33L,75L,165M) 3301.2113651.12932701. .282136916401854566106640313673268951.P44 M (3,15L,33M,75M,165L) 42888451.1020438840301.3961066561651.P64 831 (1,277) L.M L 1663.114679.1630423.11765644789597. .119504555178871023268983534947447527269739.P64 M (3) 44076407438191.P118 837 (1,3,9L,9M,31,93L,93M,279L,279M) L.M L (27M) P129 M (27L) 65324650043539.P116 843 (1,281) L.M L (3) 5059.20233.172911911281.1375848322657.14303058265301079714689773.P77 M 35407.5590415520155419.329926320009546557993324157253. .93889530611687790784978792499340162064561.P44 849 (1,283) L.M L (3) 25471. .8301611466314080069549501904096798647209210526843211654301019.P69 M 1699.6793.2312677.1597501142432086574210778580316694710747482879.P77 855 (1,3,5,15L,15M,19,57L,57M,95,285L,285M) L.M L (9L,45M,171M) 669698075470951.311642677077889231.P71 M (9M,45L,171L) 46343064339361.P90 861 (1,7,41,287) L.M L (21M,123M) 49939.65437.40412782566432403. .237114113888408583765557191645881523849.P50 M (3,21L,123L) 1723.454609.121776397.1719933601. .91763484684142928487860846109974647.P54 867 (1,17,289) L.M L (51M) 1279693.2795209.5673649.834225827263.37071429676781111221. .44345272375637763996684787.P54 M (3,51L) 494191.P125 873 (1,3,97,291L,291M) L.M L (9L) 1747.19207.408099356737585867477.P110 M (9M) P138 879 (1,293) L.M L (3) 70321.2297707.56267724103.416629385310769. .167751946286921312488219891880427162376891986493.P56 M 17581.1625466728689.9956126099416515198337.P102 885 (1,5,59,295) L.M L (3,15L,177M) 11966355914190302880887590274169088432923151.P69 M (15M,177L) 3541.153991.3239558431.6846630811.1233993275550631.P67 891 (1,3,9L,9M,11,27L,27M,33L,33M,99L,99M,297L,297M) L.M L (81L) 4269572953837417792609635043.P102 M (81M) 106921.P124 897 (1,13,23,299) L.M L (39L,69L) 52027.129169.71610909064105842601.205388305725186615253. .1451925916588584927958371446332297.P43 M (3,39M,69M) 19109689.302504188071570951181107121549176773073635506699.P72 903 (1,7,43,301) L.M L (21M,129M) 6045855901.8396466037.P101 M (3,21L,129L) 43*.3613.26628205801.38473551584154787339. .620858350010958430897.P65 909 (1,3,101,303L,303M) L.M L (9M) 1072218223.875878760011500587604133.P111 M (9L) 34543.89083.301789.8814142206721. .2115245411381559866287397735509425577692165007.P71 915 (1,5,61,305) L.M L (3,15L,183M) 7321.402601. .11680290833436277523654510517818365661993128293160111.P54 M (15M,183L) 1831.23821111.P104 921 (1,307) L.M L (3) 5527.12435343.94037544541.41544366292130993379842581.P99 M 1839136588897.P135 927 (1,3,103,309L,309M) L.M L (9M) 16378714333.248791041001.2460603909422278394029.P103 M (9L) 3709.7417.667441.14962044180614665681. .15140038547438480400123764651003503396345909.P71 933 (1,311) L.M L 11197.6126079.57673461824953153.P121 M (3) 2375632591.15789599377. .2403609388542331863112187538138617537886829.P86 939 (1,313) L.M L 5865193850703540120141889.P125 M (3) 37561.477013.P139 945 (1,3,5,7,9L,9M,15L,15M,21L,21M,35,45L,45M,63L,63M,105L,105M,315L,315M) L.M L (27L,135M,189M) 273909322011876278491.P83 M (27M,135L,189L) 17297447591971.622244499968071.P76 951 (1,317) L.M L (3) 454579.36324397.4242031875148351.110636908354198084399. .549512115983126575855924649876601277813687417.P57 M P152 957 (1,11,29,319) L.M L (3,33M,87L) 170347.63889321.1073843959.2062565445871789. .1289483195503733143.P79 M (33L,87M) 28909057.P126 963 (1,3,107,321L,321M) L.M L (9L) 75319350121.2727870992921938573.12019580563813427953015581187. .38530727715140134780820983363.P66 M (9M) 616321.1147982842062882883.130120720999646859863046577. .1018903915374204583869487996244315736990815281.P57 969 (1,17,19,323) L.M L (51M,57M) 3877.475441789.P125 M (3,51L,57L) P138 975 (1,5,13,25,65,325) L.M L (15M,39L,75L,195M) 1951.P112 M (3,15L,39M,75M,195L) 5851.12641851.91467329665270032489740651551.P75 981 (1,3,109,327L,327M) L.M L (9L) 2063874889.91755041113.P135 M (9M) 45127.38767159.33992611927399.259351671880027. .8939748369206359.3043186199715894155713.P77 987 (1,7,47,329) L.M L (3,21L,141M) 26755907602439184337475848551837359355828727.P89 M (21M,141L) 34519339.553998931060051.634553779763610143347. .18452857936885202842977571159.P60 993 (1,331) L.M L (3) 1987.617647.478405756968549949554133.P125 M 91036793334049. .15690438092853039519623397570358428793135659828199624606933.P86 999 (1,3,9L,9M,37,111L,111M,333L,333M) L.M L (27L) 2615383. .792615901665390921359533539904938817776371948323522457540677.P89 M (27M) 1999.7993.48366655669261.P134 1005 (1,5,67,335) L.M L (15M,201M) 2011.739828812361.2709644468095958739571. .396067351989170036074128364869717451081.P51 M (3,15L,201L) 1648757425261.114930794313903734467877618236500915404671.P74 1011 (1,337) L.M L 10111.475422088807. .40017666590749974337826438228229397342408512612651846790009.P87 M (3) 296768007466640363281.118311296994193648484589397.P114 1017 (1,3,113,339L,339M) L.M L (9M) 8342589313.915099621078019541370469051218219809941501498141.P103 M (9L) 258319.4759561.423195294979.249504620848655097819331. .16211062842493949016958272244358278685152181951173.P65 1023 (1,11,31,341) L.M L (3,33M,93L) 19174858828306360645533450526720857649051. .19337980565378171534889993094421861389450501.P60 M (33L,93M) 82325575332463.916226106737897927533. .1575155207429963661696683189664217.P75 1029 (1,7,49,343) L.M L (3,21L,147M) 7*.48517052647620607.P123 M (21M,147L) 374557.596821.43130485963642981.9062940254538824227819939. .3354356969043817266850856322523231704213187.P45 1035 (1,3,5,15L,15M,23,69L,69M,115,345L,345M) L.M L (9M,45L,207M) 20544192840232981974341524541641114431739055519477161.P74 M (9L,45M,207L) P126 1041 (1,347) L.M L 6892793323373912358814239820687. .254139660710314265859242122277843290934557. .2027489666453382580690006167619461409824120037.P49 M (3) 2083.5377807.627786296577630424677374928673489378204215295\ 65882574678483317963541237.P84 1047 (1,349) L.M L 6271848287482534909.P148 M (3) 60727.77479.898327.2770820587.4607768568088467088485731928\ 91152036252965685853508369019636063025441.P72 1053 (1,3,9L,9M,13,27L,27M,39L,39M,117L,117M,351L,351M) L.M L (81L) 381350269.828864739.14770982235456815760466328504017. .23879893447642484359783138389093155014728859.P63 M (81M) 21061.365426184943.P139 1059 (1,353) L.M L (3) 79615621.2367719063763857822934247. .195570061420579042031041088952820573. .500258793716411748689797558450829549801989.P59 M P169 1065 (1,5,71,355) L.M L (3,15L,213M) 4261.22362247200781.P118 M (15M,213L) 63901.432391.153492061.P115 1071 (1,3,7,17,21L,21M,51L,51M,119,357L,357M) L.M L (9L,63M,153M) 2143.402777955417573.36954556187808421. .64876583110042176390667.808469860665849095653200462979.P51 M (9M,63L,153L) 736437756465937.P123 1077 (1,359) L.M L 318793.409261.3668263.1276578871.60311487349.127112425273.P123 M (3) 803443.518094843517.1205494272636831421987. .44779485581193256543637836329731095292692846473629922755299.P74 3^{3h}+1=(3^h+1)L.M, L=3^h-3^k+1, M=3^h+3^k+1, h=2k-1. Table 5- Factorizations of 5^n-1, n odd, n<376 L,M for n=10k-5<=745 n Prime Factors 1 2.2 3 (1) 31 5 (1) L.M L 11 M 71 7 (1) 19531 9 (1,3) 19.829 11 (1) 12207031 13 (1) 305175781 15 (1,3) L.M L (5M) 181 M (5L) 1741 17 (1) 409.466344409 19 (1) 191.6271.3981071 21 (1,3,7) 379.519499 23 (1) 8971.332207361361 25 (1,5L,5M) L.M L 9384251 M 101.251.401 27 (1,3,9) 109.271.4159.31051 29 (1) 59.35671.22125996444329 31 (1) 1861.625552508473588471 33 (1,3,11) 199.386478495679 35 (1,7) L.M L (5M) 85280581 M (5L) 211.631.4201 37 (1) 149.13971969971.8737481256739 39 (1,3,13) 79.608459012088799 41 (1) 2238236249.5079304643216687969 43 (1) 1644512641.172827552198815888791 45 (1,3,9) L.M L (5L,15M) 1171.169831 M (5M,15L) 297315901 47 (1) 177635683940025046467781066894531 49 (1,7) 227376585863531112677002031251 51 (1,3,17) 90271.317731.654652168021 53 (1) 5960555749.17154094481.27145365052629449 55 (1,11) L.M L (5L) 11*.103511.190295821 M (5M) 511831.65628751 57 (1,3,19) 11735415506748076408140121 59 (1) 21180247636732981.2047572230657338751575051 61 (1) 8419.918585913061.140194179307171898833699259 63 (1,3,7,9,21) 280729.2161279.23792163643711 65 (1,13) L.M L (5M) 20986207825565581 M (5L) 131.1034150930241911 67 (1) 269.1609.26399.2454335007529.604088623657497125653141 69 (1,3,23) 139.6211.598761682261.8868050880709 71 (1) 569.18607929421228039083223253529869111644362732899 73 (1) 4853479.5729041.9519524151770349914726200576714027279 75 (1,3,5L,5M,15L,15M) L.M L (25M) 151.3301.183794551 M (25L) 1989151.49892851 77 (1,7,11) 527093491.8090594434231.162715052426691233701 79 (1) 205367807127911.58523123221688392679.344120456368919234899 81 (1,3,9,27) 4861.11419697846380955982026777206637491 83 (1) 20515111.1431185706701868962383741.88040095945103834627376781 85 (1,17) L.M L (5M) 8198241112969626815581 M (5L) 1531.34563155350221618511 87 (1,3,29) 5569.6961.28870194250662203210437116612769 89 (1) 179.9807089.14597959.834019001.8157179360521.231669654363683130095909 91 (1,7,13) 9680647790568589086355559.17499733663152976533452519 93 (1,3,31) 31*.148429.878851.172974812463239310024750410929 95 (1,19) L.M L (5L) 2851.11600321878916922053491 M (5M) 4113691.1245576402371959291 97 (1) 389.264811.P60 99 (1,3,9,11,33) 143551.1731511.22542470482159.153560376376050799 101 (1) 5937018283241.3434487311396589821473854121.P30 103 (1) 3709.28429.59117897713198738371603984809.P35 105 (1,3,7,21) L.M L (5L,15M,35M) 21226783250214361 M (5M,15L,35L) 1736701.119461537021 107 (1) 6421.5486016363791.35411885288978941.172163150940018661.P24 109 (1) 1091.1007161.1528399.P61 111 (1,3,37) 3109.P47 113 (1) 2939.6329.129499.308491.304247586761.2084303944451. .620216264269531.8237123176890810696379 115 (1,23) L.M L (5M) 689081.29028071.100062970166640331 M (5L) 461.691.2855911.824480311.17223586571 117 (1,3,9,13,39) 223963741.P42 119 (1,7,17) 239.1429.4999.7497182681291140146079.P36 121 (1,11) 12101.486179.P68 123 (1,3,41) 739.960139.1785961.9025583299.P31 125 (1,5L,5M,25L,25M) L.M L 3597751.P29 M 28707251.4032808198751.767186663625251 127 (1) P89 129 (1,3,43) 18471511.43955934961951833386625799.P26 131 (1) 2621.23928199.34720241.16815642611861.P60 133 (1,7,19) 9311.65171.281429.3257947519.152317058321.P41 135 (1,3,9,27) L.M L (5M,15L,45M) 11071.1312315694449748688331 M (5L,15M,45L) 541.26941244373060650224561 137 (1) 20551.603349.48102071.121719631478506669.7851027307722624763151.P39 139 (1) 21521602057721.6789441546024769741462601111.P56 141 (1,3,47) P65 143 (1,11,13) 24615836446631.53130566763791958299.P51 145 (1,29) L.M L (5L) 1461311.P34 M (5M) P39 147 (1,3,7,21,49) 24556351.5071357999.2035895040229.P30 149 (1) P104 151 (1) 1175989.2237519.389439261961.12799319666401. .2843809592323334251225153490677489.P35 153 (1,3,9,17,51) 4591.26481241.360143672909416579.P39 155 (1,31) L.M L (5L) 11161.257611.31473312961.21783999170235219053011 M (5M) 311.5624951.P33 157 (1) 32029.5129819.2107089779.8616314452100494153901371725720169.P55 159 (1,3,53) 1775305720077559.P58 161 (1,7,23) P93 163 (1) 4599209.40100609.675775181.6582151087844246659. .102556399583828574447011133455059.P40 165 (1,3,11,33) L.M L (5M,15L,55M) 2311.P26 M (5L,15M,55L) 331.9867165115635267180926131 167 (1) 18371.53441.P108 169 (1,13) 13859.784646826705980283039372085276899721.P70 171 (1,3,9,19,57) 19*.P75 173 (1) 1039.3461.1708272343265311.P99 175 (1,5L,5M,7,35L,35M) L.M L (25M) 28001.200201.8894201.P26 M (25L) 12601.50051.22661801.1657309151.38105263380318401 177 (1,3,59) 198241.340863370420651571324835367261.P47 179 (1) 359.3581.75539.17315029.100894073362387242965129.P84 181 (1) P126 183 (1,3,61) 38431.P80 185 (1,37) L.M L (5M) 2591.P47 M (5L) 30810641.21829321837586441.P27 187 (1,11,17) 4200769.1202338040280510524134632541097924516136661.P64 189 (1,3,7,9,21,27,63) 305921358183421.P62 191 (1) 112691.60426671.P121 193 (1) 749154725101.406875383561091922623241829.P96 195 (1,3,13,39) L.M L (5L,15M,65M) 14821.P29 M (5M,15L,65L) 933692761.P26 197 (1) 470323176131.362204827770839.P111 199 (1) 53731.P134 201 (1,3,67) 1248228732195063112609361470351.P63 203 (1,7,29) 493291.4978655062910170670969991331.P84 205 (1,41) L.M L (5L) 15991.1256950067521.P40 M (5M) P56 207 (1,3,9,23,69) 10047916621.P83 209 (1,11,19) 419.56431.P119 211 (1) 5594292675731.37973612258438259769.2047676978710884689089. .144115393066310961947385445876092809.P59 213 (1,3,71) 156309592445437909.P81 215 (1,43) L.M L (5M) 1291.P56 M (5L) 431.144982241.1273316896028212631.P31 217 (1,7,31) 8681.1828916514769.P110 219 (1,3,73) 439.429241.2183431.239701757320911389817996792709.P57 221 (1,13,17) 351391.231452141519.183276094190104631834639. .1436003589550079403417985191612889433318011249.P49 223 (1) 355909.P150 225 (1,3,5L,5M,9,15L,15M,45L,45M) L.M L (25L,75M) 1274851.1390332823651.489346511141264975761501 M (25M,75L) 1086749551.P33 227 (1) 863773591.17408515139.107857890714179.154907695140797990849. .239976686263858506551.16831369699997499687405534401.P57 229 (1) 2749.53129.63785116081353654247759.25703365361608909110896940589.P101 231 (1,3,7,11,21,33,77) 13920748381.267859557529209897722406319386619.P42 233 (1) 1318781.412500871.208771951788632309319091684496790985222571. .122893706196784651098718052024745515496783278694509.P57 235 (1,47) L.M L (5M) 20885861.68308861.P49 M (5L) 941.4231.96766610646500911.P42 237 (1,3,79) 12799.657439.447298617719114285037649.P76 239 (1) 479.40093613041379.P151 241 (1) 79531.578401.882061.464913101.128338427949683383916242111. .23296571833941039118079506609079.1054929344030207429836604785995221.P53 243 (1,3,9,27,81) 1459.14001661.P103 245 (1,7,49) L.M L (5L,35M) 491.8821.10781.P49 M (5M,35L) 16650328910366149531471.P37 247 (1,13,19) 29641.893134065430622331883159985777080426121. .73264607998188798376620748253610482190769.P67 249 (1,3,83) 499.12451.169321.64613577662440706821. .486307761332920261532701.P60 251 (1) 8325671.31005529.P161 253 (1,11,23) 215556321311.4586605887769406257148888900423581. .75458741165755163938354406143932160485170968091.P62 255 (1,3,17,51) L.M L (5L,15M,85M) 1021.1445377105917001.P27 M (5M,15L,85L) 236641.782302186051.38385602257801.263420722813531 257 (1) 10081392432072125477404185330039079.P146 259 (1,7,37) 1483253451821989.12331512430205535516641371.P111 261 (1,3,9,29,87) 6717619.81131329.420610743056505018221215111.P77 263 (1) 1523516701711.P172 265 (1,53) L.M L (5M) 488094322309591.1335618937071191.P43 M (5L) 1061.43347650492220877561107611.P45 267 (1,3,89) 1069.1133149.1652731.18484574880511.369718501929859. .92358800604937937130124908509003639071.P42 269 (1) 3229.4016171.32785719659723694619.P158 271 (1) 64993931.12987902099.P171 273 (1,3,7,13,21,39,91) 376909369155066379919582224252183771.P66 275 (1,5L,5M,11,55L,55M) L.M L (25L) 23785874550224051.29881163609373451.43877290026688801.P21 M (25M) 233201.1234133939501.354655233566701.P38 277 (1) 37095841.14075563135476669013895019180975816431.P149 279 (1,3,9,31,93) 247114592858611.P112 281 (1) 631100202961413821.P179 283 (1) 1699.451669.113334709.416742821994932569.33926661157694104397239. .1503555624642039390353881.8717585253517894966154284413195420314854559.P73 285 (1,3,19,57) L.M L (5M,15L,95M) 30211.260930841421.P35 M (5L,15M,95L) 571.P48 287 (1,7,41) 10690751.203375089.1038891585945814650631.P132 289 (1,17) 17341.81053519.27605542907603789.9027110169772242694759.P140 291 (1,3,97) 8731.15247819.65482996292971.425798685220729.P95 293 (1) 1759.520369.224108738217451.88957588316686547560127731.P155 295 (1,59) L.M L (5L) 842521.6264826343527027047964986594326671.P42 M (5M) 1448181445390051.485704102682442915241.P45 297 (1,3,9,11,27,33,99) 1049599.1730583185128108939. .101367829967676409195407966079.P73 299 (1,13,23) 599.71761.1076401.7752619982267966542535041531665354400879. .4483622187767180916663396803931609479674368941155912707479.P74 301 (1,7,43) 66221.3595452428681.453098474981964966729037498128705243871.P121 303 (1,3,101) 126463111. .897449797190508611732321830427288714681382628177991026939.P75 305 (1,61) L.M L (5L) 1884901.P78 M (5M) 1831.2441.1786560207910631.117369445599178322177831741.P36 307 (1) 30093907237519.41907329770349. C187 309 (1,3,103) 619.8934148519.42173111702521341940416989340041084225191.P90 311 (1) 263729.1649908341047346424876131429988519619911. C173 313 (1) 229651231. C210 315 (1,3,7,9,21,63) L.M L (5M,15L,35L,45M,105M) 11971.23311.34651.P38 M (5L,15M,35M,45L,105L) 1732501.P45 317 (1) 34871.29048967458203698934091. C194 319 (1,11,29) 95701.533942839. C182 321 (1,3,107) 35311.80251.3482851. .204438681420686525733014991351502624422714996979.P85 323 (1,17,19) 3247691391126251. C186 325 (1,5L,5M,13,65L,65M) L.M L (25M) 1659451.142816611356873351.P61 M (25L) 1641395317366745868848220671801.P54 327 (1,3,109) 3900606421.2570834326384926058220919782123933663342371.P99 329 (1,7,47) 659.6581.15957217104409233285978673415179. C155 331 (1) 67440292875072467734808551587718580464816759. C187 333 (1,3,9,37,111) 15319.344145511. .11071665290671449530331408923856186107268916092023773607149.P81 335 (1,67) L.M L (5M) 126631.11494162725571360186894779691.P59 M (5L) 1148552280514941389076611.P69 337 (1) 242550562936636678266163293887551.P203 339 (1,3,113) 7459.234303241.22628763748399.204867325883294509. .24528557597575188455414632667311.P83 341 (1,11,31) 109121.10161119.192446105281.609146164309. C175 343 (1,7,49) C206 345 (1,3,23,69) L.M L (5L,15M,115M) 21391.31741.1715341.27875688121.P36 M (5M,15L,115L) 37951.5347963681.2351881115374174051.P30 347 (1) 34911671.9060198312365106899848549. C210 349 (1) C244 351 (1,3,9,13,27,39,117) 7655311. .6475711850365695029787483033056414199292785571. .1489161023006154219903790225805356280792802449809.P51 353 (1) 235099.5451190499.205504553260781.34785215885504832719. C198 355 (1,71) L.M L (5L) 8499626476216091.8558727566683804731617356972960527829841.P43 M (5M) 71*.17041.7484111.P85 357 (1,3,7,17,21,51,119) P135 359 (1) 719.41785692653578003162849.6677881008782967997903339939. .837248571667848555569202584041.P168 361 (1,19) 129422865652104096162599.6417463808715658282089494909. C189 363 (1,3,11,33,121) 3631.P151 365 (1,73) L.M L (5M) 1077334433621.11219338425853865221726037921.P61 M (5L) 6571.1328865721.650916499741.22354588958731.33735961890251. .560294380367699191.P32 367 (1) 1047157937929.645658411286666140609459. .52862043959452141411641760543741.P189 369 (1,3,9,41,123) C168 371 (1,7,53) 2969.11131.35922655704041.226578241537144915139. .11014814494800487352604755748091574916119.C137 373 (1) 2239.4350204259.1368671486390599.437284546695919489287780329. C206 375 (1,3,5L,5M,15L,15M,25L,25M,75L,75M) L.M L (125M) 751.317286001.527559073501.P47 M (125L) 281057814001.38033863525621501.P42 ------------------------------------------------------------------------------- 385 (1,7,11,77) L.M L (5M,35L,55M) 33411357084712191971.P65 M (5L,35M,55L) 2471701.927476143441.134234460550630441.P49 395 (1,79) L.M L (5L) 104449388937445035371.P90 M (5M) 190391.68175421.38701052851841.6440862401422039384631.P61 405 (1,3,9,27,81) L.M L (5L,15M,45L,135M) 811.1621.6481.921737881.P57 M (5M,15L,45M,135L) 2332368714077641.279151346689444799703543961.P34 415 (1,83) L.M L (5M) 116201.90045041.167674286348441.20498545382037148227331. .84340842933027824154067061.P39 M (5L) 1209311.P109 425 (1,5L,5M,17,85L,85M) L.M L (25M) 5101.3609101.P102 M (25L) 4878161432677729051.P94 435 (1,3,29,87) L.M L (5M,15L,145M) 22621.646325611.81097049492978072251.P46 M (5L,15M,145L) 5931661.195347093735677589850742253611.P42 445 (1,89) L.M L (5L) 26701.26698816301.103738789930024471.P92 M (5M) 8011.15131.101232724284574681.14542112049750708402496286411251.P67 455 (1,7,13,91) L.M L (5L,35M,65M) 252009190957922611927192988424665484581951479831.P53 M (5M,35L,65L) 911.4914911.6481021.P85 465 (1,3,31,93) L.M L (5M,15L,155M) 18918352942471114958730682051.P57 M (5L,15M,155L) 2791.6084353978581.385988764693732689151104968796091.P35 475 (1,5L,5M,19,95L,95M) L.M L (25L) 1954151.P120 M (25M) 11360856146437080511603913201. .11971699680363533589698621027808346660430201.P55 485 (1,97) L.M L (5M) 971.2387171.286948574407858827947671. .4064396828893513244260225706548054644512772987091.P53 M (5L) 3881.12611.5829701.11401381.4588270721.P104 495 (1,3,9,11,33,99) L.M L (5L,15M,45L,55L,165M) 578259991.P76 M (5M,15L,45M,55M,165L) 991.19801.14300545887541. .123624849246637675534237287451.P35 505 (1,101) L.M L (5L) 205031.520151.656821011757186571. .36690330713871434099552140344241171.P77 M (5M) 5051.671651.119524411.9476228324821. .22556231631518418786932381290161151.P75 515 (1,103) L.M L (5M) 1031.96821.326493403069610501.87332225947582956902696341. .8693112016386012208667474531956646459249501.P48 M (5L) 41201.236985509596761461.56727322344599853862293969440589550231.P84 525 (1,3,5L,5M,7,15L,15M,21,35L,35M,105L,105M) L.M L (25L,75M,175M) 1051.P81 M (25M,75L,175L) 37815352051.P74 535 (1,107) L.M L (5M) 618691336713427778212600657181.277267461900868216455231985933091.P86 M (5L) P149 545 (1,109) L.M L (5L) 232171.21519871.222583733401.P128 M (5M) 1102582961.2392268400751445411411.197279999499978473755531. .2602111035179418475927861.P73 555 (1,3,37,111) L.M L (5L,15M,185M) 12211.154402111.9202869825377571330816454640823938251.P51 M (5M,15L,185L) 156511.834721.19852351.P83 565 (1,113) L.M L (5M) 81119810875491958307893501.P131 M (5L) 17317559621.578904334643163991518185302373441.P114 575 (1,5L,5M,23,115L,115M) L.M L (25M) 201781301.59383718252771389151.31766207470090423211256551886690151. .8681684850386430151422007197514419601.P55 M (25L) 1151.173651.1069501.40231601.26135496851. .3190505517374665681595009461154083852963479431101993034851.P64 585 (1,3,9,13,39,117) L.M L (5M,15L,45M,65L,195M) 5648761.945078093181.1016644491721.P70 M (5L,15M,45L,65M,195L) 2497240172701.7845827291641.P76 595 (1,7,17,119) L.M L (5L,35M,85M) 23801.25970709103346701.9538501024577801535193513460771.P83 M (5M,35L,85L) 3597764176982506745587150886060717612102325001.P90 605 (1,11,121) L.M L (5L,55L) 11*. C153 M (5M,55M) P154 615 (1,3,41,123) L.M L (5M,15L,205M) 1231.2908888501.1788582600145862687626441.P76 M (5L,15M,205L) 62731.248461.18383372131.226073665516341068071.P71 625 (1,5L,5M,25L,25M,125L,125M) L.M L 637043435256965381251.887918028727761332501.P133 M 1122853751.P166 635 (1,127) L.M L (5M) 39371.1291779384590714829718240121. C144 M (5L) 702206150831.5598493819552929453451. .12318542415046443477661711361.P115 645 (1,3,43,129) L.M L (5L,15M,215M) P117 M (5M,15L,215L) 1269509641.4144987978415039132191. .3118954401781386053150022153343306501.P51 655 (1,131) L.M L (5L) 14411.592121.601291.2304799900471. .9401087165312249425680125005501.P124 M (5M) 18341.51703081.799726387996561. C155 665 (1,7,19,133) L.M L (5M,35L,95M) C152 M (5L,35M,95L) 347131.426361515667769851699539882056479395496411.P104 675 (1,3,5L,5M,9,15L,15M,27,45L,45M,135L,135M) L.M L (25M,75L,225M) 14851.71551. .224491256466428912635990400917424912842296807654322501.P64 M (25L,75M,225L) 1357803001.8227149935929283044132471512207436501.P80 685 (1,137) L.M L (5M) 18025611971.535569744943399716958855013333971.P147 M (5L) 497478532938871159260123601.5276583832843396532095802023230871.C131 695 (1,139) L.M L (5L) 10170631.460503727624584883373804093554831. .6361052470423138945814073705227461.P120 M (5M) 822881.28927420661.9807083838590469822562651. C152 705 (1,3,47,141) L.M L (5L,15M,235M) P129 M (5M,15L,235L) 1290151.43779091.40130368419540180043461725371.P87 715 (1,11,13,143) L.M L (5M,55M,65L) 2861.15731.568219795001.1835752527181.4734577062931. .15650665725833711.P108 M (5L,55L,65M) 7151. C164 725 (1,5L,5M,29,145L,145M) L.M L (25L) 1451.21751.1526625921911039333504551. C165 M (25M) 97151.508005163062054101.2986825327584332523851. .1402006809136700630208151.P128 735 (1,3,7,21,49,147) L.M L (5M,15L,35L,105M,245M) 1471.12388179201301. .69883849889109985909137301.2330833648199530366716543767343661.P42 M (5L,15M,35M,105L,245L) 72031.56117251.P105 745 (1,149) L.M L (5L) 8941.444296944929401474501177110211288771. C168 M (5M) 674865871526349844777781.862749058814541800048281. C159 5^{5h}-1=(5^h-1)L.M, L=T^2-T.5^k+5^h, M=T^2+T.5^k+5^h, T=5^h+1, h=2k-1. Table 5+ Factorizations of 5^n+1, n<=375 n Prime Factors 1 2.3 2 2*.13 3 (1) 3*.7 4 2*.313 5 (1) 521 6 (2) 601 7 (1) 29.449 8 2*.17.11489 9 (1,3) 3*.5167 10 (2) 41.9161 11 (1) 23.67.5281 12 (4) 390001 13 (1) 5227.38923 14 (2) 234750601 15 (1,3,5) 61.7621 16 2*.2593.29423041 17 (1) 3061.41540861 18 (2,6) 37.6597973 19 (1) 761.19609.213029 20 (4) 241.632133361 21 (1,3,7) 7*.43.127.7603 22 (2) 89.1030330938209 23 (1) 47.42272797713043 24 (8) 152587500001 25 (1,5) 1901.50150933101 26 (2) 13*.53.83181652304609 27 (1,3,9) 3*.163.487.16018507 28 (4) 59509429687890001 29 (1) 5096867.6090817323763 30 (2,6,10) 2281.69566521 31 (1) 1303.21207101.28086211607 32 2*.641.75068993.241931001601 33 (1,3,11) 595123.190771747 34 (2) 1973.20129.45289.12447002677 35 (1,5,7) 15216601.4698932281 36 (4,12) 73.543097.1503418321 37 (1) 9103.29010221.45920153384867 38 (2) 4885168129.2864226125209369 39 (1,3,13) 3121.22735632934561 40 (8) 25601.909456847814334401 41 (1) 83.43543.221401.9472026608675509 42 (2,6,14) 2521.24587411156281 43 (1) 1549.9547.7866608083.1628744948329 44 (4) 9080418348371887359375390001 45 (1,3,5,9,15) 60081451169922001 46 (2) 5465713352000770660547109750601 47 (1) 2069.15888756269.3602372010909260861 48 (16) 97.240031591394168814433 49 (1,7) 49105547.1866013003.2481357870461 50 (2,10) 239201.424256201.89620825374601 51 (1,3,17) 103.8467.528667.60119016343 52 (4) 51169.537181587281.129044008326199409 53 (1) 107.28838378869.599659003321309822423087 54 (2,6,18) 14551915228363037109375001 55 (1,5,11) 10910444855403996246103496881 56 (8) 113.337.2520917617.37007700327977836913 57 (1,3,19) 229.75649382555448580095589 58 (2) 1334402673828313149547634216455312875601 59 (1) 827.5242462229.3237765225301.2059647179472887 60 (4,12,20) 23320317172851318360001 61 (1) 367.9029.15571335384347.14008364639128540436401 62 (2) 8124604717965111529.102651353523520067851969 63 (1,3,7,9,21) 883.406729.24132781.1692416503 64 2*.769.3666499598977.96132956782643741951225664001 65 (1,5,13) 18461.15188886343541.15199221608544481 66 (2,6,22) 1453.6509387183417404924784917 67 (1) 11293772630057337854244300009061892827351888021 68 (4) 137.623017.938894988049.1361753880209.4959636586609 69 (1,3,23) 66163549.253592389.403316413944121 70 (2,10,14) 281.13148832195720299503896018648521 71 (1) 4261.5747338499820296170481.288231038713838413442281 72 (8,24) 1297.2739177855667309845605995807633 73 (1) 63554310563.777612767772190289.3570677866897550288203 74 (2) 9769.40849.510241095096183757930733363918820917976121 75 (1,3,5,15,25) 118801.20775901.24665701.149439601 76 (4) 457.21363981507860375753.21654472202540732126905077281 77 (1,7,11) 20828886541.49970061516036179615325895945741 78 (2,6,26) 157.8684521.4056854881.667929705480493 79 (1) 18251687.7897663181.511465533067.37399095525167136010188229 80 (16) 131349761.167597261761.24625444126052524088217281 81 (1,3,9,27) 3*.1783.5023.2066067271380136212224701233463 82 (2) 193357.6355001.1148205782281.56373078952722628530598981268453 83 (1) 167.4029666108840585686296627.2560787702841639767474730913969 84 (4,12,28) 6553.90217.6019022585035590658668001 85 (1,5,17) 75752681.247515241.504156421.68795069664507129341 86 (2) 173.2171388367013.132331554743163541916284364878460504933118649 87 (1,3,29) 349.210390487070809.22500358133965991972941 88 (8) 13729.929281.71225159567951317923809.91029014606406186465761 89 (1) 39387996609449861.56522267529181963.12094715786677995586454978647 90 (2,6,10,18,30) 20478961.6794091374761.25535754811081 91 (1,7,13) 15887476811320661.15994146485373751289418997754783021 92 (4) 150220315444217.214752088491462210591995581828628861192144614553 93 (1,3,31) 258065887.75005167927.53345671490722200466369 94 (2) 5077.12409.329573417220613.935213864500231208652603316429973471246089 95 (1,5,19) 4561.179763436784239734042181.309828362361188845069741 96 (32) 193.5207826497153857.539344757336151926206665601 97 (1) 29683.261707.547663.90130760102421063383.P32 98 (2,14) 197.164204573839769.74535675530760254357.21441970593484574539001 99 (1,3,9,11,33) P42 100 (4,20) 4001.132001.776401.P42 101 (1) P70 102 (2,6,34) 6733.4613053.19724557.34288117.26837241260899651321 103 (1) P72 104 (8) 247161617.825256433.2220784177.31308249137777.P27 105 (1,3,5,7,15,21,35) 421.5236141.1354224218968567573270561 106 (2) 8871726015923707071209.P51 107 (1) 643.P72 108 (4,12,36) 73009.1853281.3314953.36280398313.13012873776055827785521 109 (1) 19403.4046322895447485867367.P50 110 (2,10,22) 245521.1458601.2802204291103029121.P26 111 (1,3,37) 223.5107.668221.13844587.107903101.221746234901611997486023 112 (16) 271489.1149569.10922689.465314420407473281.P31 113 (1) 227.1387189.12249784663.P60 114 (2,6,38) 22573.53590717.2108505761893.P26 115 (1,5,23) 73141.P57 116 (4) 233.929.33409.397823386118610689.1547355341777494553.P33 117 (1,3,9,13,39) 40483.43236180703.P36 118 (2) P82 119 (1,7,17) 2381.25229.4172141.P53 120 (8,24,40) 2172116161.P36 121 (1,11) 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138485881.1391925191575724209.P75 235 (1,5,47) 14975141.25019393608870061.7469015808480614081.P87 236 (4) 1889.66553.38710282321.P144 237 (1,3,79) 1423.53089.787597927.3620406337123.51977539194197989.P64 238 (2,14,34) 2237307921069778921841.P113 239 (1) 17209.5729889967417247. .1003240831021866550564937680732854800270693763847709.P96 240 (16,48,80) 582954476493740838084778148633415817921.P51 241 (1) 1447.271849.533122367.525411589067580318444083. .366585579705641176488670059469.P98 242 (2,22) 30493.9916251976518642052563357297077883532184524093.P104 243 (1,3,9,27,81) 3*.8263.39367.17995609.985562803.5986535931982369. .83881765148602365370510261987969.P41 244 (4) 57097.1475034311407732073353.P142 245 (1,5,7,35,49) 114661.187181.5758481.20334022013834451721. .194043546506490017613781.1935635465952890802398761.P34 246 (2,6,82) 4560841.65465466516157.P92 247 (1,13,19) 4447.5853901.29599987.5513798691623.6655472266225553901469. .14120148037454873337452770514154962809.P62 248 (8) 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C203 312 (8,24,104) 1249.1873.293876827247645824001934037873.P99 313 (1) 4321661135227604368687. C197 314 (2) 15980089.388038314748637665126113925790477. C179 315 (1,3,5,7,9,15,21,35,45,63,105) 35281.69850912140360790741.P77 316 (4) 1195838801.10005578153.70432242073.82932824137.P178 317 (1) 4084229.172992716783529233443.3620382004977001942052983. C170 318 (2,6,106) 19081.20947933.436276206825076349879647249. .110948582559121653141616707828218569.P73 319 (1,11,29) 28476798241.76276878979955184439531431817934729.P151 320 (64) 17921. C175 321 (1,3,107) 2303573383935650005163767.273860673667943993469496783. .15508073443324126840152709489.4753712821254698015771925989227.P39 322 (2,14,46) 1289.424397.4195885464702037.1198400376705575705576881. .12658289026799429610110288303852317. .37458200184731560512972757879121310733.P65 323 (1,17,19) 647.18089.727007771958290921190121741. C168 324 (4,12,36,108) 209290024478377.177309277461360218309390137951788241. .14448621958263887100257660421295942561.P65 325 (1,5,13,25,65) 1301.2024275501.31306627301.P145 326 (2) 653.2609.189895001.23288351985517693013. .25666218950437934848265249.836678744221945580045751077.P141 327 (1,3,109) 10787032338307.16566453047149.24753046968859330729. .29680517470861398776947048909.23801279212976547698450531783389.P46 328 (8) 17713.20907377.94877599143390227898211503024977. C181 329 (1,7,47) 2549057618736721.13563720869035756711741. .19140345898931565956181098154647.P125 330 (2,6,10,22,30,66,110) 1321.4411608961.P100 331 (1) 48989.274069.404483.35098027085436321411407. C193 332 (4) 2058554713.65438094203676554432094356953. .92204567651115096086964349490379361.P157 333 (1,3,9,37,111) 8260482604912643089.25085679215566320053389. .20880879276654535886445179571008053406388481.P67 334 (2) C233 335 (1,5,67) 6701.628301435347801.3337802987674672671171503141. .4813691646990247186027072585399061245861.P99 336 (16,48,112) 673.2689.8906835789071809.P112 337 (1) 99347042703101.8681942880812709284936701.P196 338 (2,26) 13*.677.349709778373997142089.452629512771138390982997. .4020226117864755963006649.1314711044344945942445899409. .68455761994776074550081198997.P90 339 (1,3,113) 18307.4392763.2987233423.117825760147.16509399574192003102207. .457225664132454497901028516937139615332312607324601.P53 340 (4,20,68) 8161.17681.48886055402391862040941201. .11441045552404091443187740021633178237681.P106 341 (1,11,31) 683.21143.3055305555941.853869447408847.2846800854247901. .1926361897054962585928331464880223029383.P121 342 (2,6,18,38,114) 50164561.197991079813.90492378184051683013. .17095269917121096397448449. .7429367931326116783831780610130726189759289.P44 343 (1,7,49) 15078281.670548333797224163.497030883351192430344613753441. .705782575459215386450100057697624063.P115 344 (8) 183399473.3070535057. C218 345 (1,3,5,15,23,69,115) 1381.43100384224227086881. .163263999306942963967949719201.P71 346 (2) 3379037.1490847569.2133076820179418693. .1611335060191887691514988317272249.C174 347 (1) P242 348 (4,12,116) 19316392153.26160681101041.701570688430849. .867521757880801.5163011441108401.2062003172288320153.P70 349 (1) 8942070323.699603551730901.3562202055870367855123667. C194 350 (2,10,14,50,70) 21001.4813889390953505801.P145 351 (1,3,9,13,27,39,117) 87049.3771847.P140 352 (32) 1409.369059329.P212 353 (1) 4943.1492860183629. C231 354 (2,6,118) 23662955437126651591573. C140 355 (1,5,71) 65672997381060914413551821. .30535022092590033631541127783262141.C136 356 (4) 2137.187090930562706936930665593.840552573146809635459322735649.P187 357 (1,3,7,17,21,51,119) 9283.P131 358 (2) 12227975198457533. C233 359 (1) 14870544741210523.P234 360 (8,24,40,72,120) 30241.43201.471354274081. .79940197070487174977181201851988481.P79 361 (1,19) 140069.59588684185483. C221 362 (2) 154213.2533277. C241 363 (1,3,11,33,121) 727.P151 364 (4,28,52) 6165310743305738342794703714473897.P168 365 (1,5,73) 497997249288521.143360969004690255541.P167 366 (2,6,122) 1852487492507928532657573. C144 367 (1) 73219364069.70057995652034894429. C226 368 (16) 22817.3391255113651617.7673924820048666337.38355937362039743393. .1181985669274649173537.C167 369 (1,3,9,41,123) 10483773125218147. C152 370 (2,10,74) 1481.5121318001. C189 371 (1,7,53) 743.31907.171403.42073627.2340865442872909. .83529561196595406306863.4294105917163012848027061867115931367. .241881732025657819145103362017436952827107.P82 372 (4,12,124) 854099353.P159 373 (1) 16827523.855947877694729.3402270307745780791746163. C214 374 (2,22,34) 36653.1833280694213.273799167334154011397. C187 375 (1,3,5,15,25,75,125) 9001.994501.84719274001.P119 Table 6- Factorizations of 6^n-1, n odd, n<330 n Prime Factors 1 5 3 (1) 43 5 (1) 5*.311 7 (1) 55987 9 (1,3) 19.2467 11 (1) 23.3154757 13 (1) 3433.760891 15 (1,3,5) 1171.1201 17 (1) 239.409.1123.30839 19 (1) 191.638073026189 21 (1,3,7) 1822428931 23 (1) 47.139.3221.7505944891 25 (1,5) 5*.18198701.40185601 27 (1,3,9) 163.623067280651 29 (1) 7369130657357778596659 31 (1) 5333.49744740983476472807 33 (1,3,11) 67.45686117391553 35 (1,5,7) 71.37863211.1469029031 37 (1) 149.7919.12211.2569799.334286825813 39 (1,3,13) 3143401.1262014275211 41 (1) 8648131.1854850885886497427178961 43 (1) 173.431.7383359.1048953903129961695599 45 (1,3,5,9,15) 2161.112771.19353635731 47 (1) 930911329.45110836129.17821718159716147 49 (1,7) 6527977.122694573317.600827908214213 51 (1,3,17) 307.927037099.23412002806867 53 (1) 13781.357293834576449.7091531088740602980647 55 (1,5,11) 3675127061.3031462959351050977391 57 (1,3,19) 47881.820459.219815829325921729 59 (1) 4866979762781.29050941569087.11522163007228653937 61 (1) 42461491.80057377.17252803354297421346943980322273 63 (1,3,7,9,21) 379.8387947.616332907.5239858051 65 (1,5,13) 11831.1420901.49398961.22533649654910414281 67 (1) 904949028329910415467529.3023706637809542222940030043 69 (1,3,23) 11731.1236385853432057889667843739281 71 (1) 3546245297457217493590449191748546458005595187661976371 73 (1) 44764549877.2436094907761.8439148071138817.138721648424756087 75 (1,3,5,15,25) 601.82051.271041511600591342728451 77 (1,7,11) 484847574510970082567.84002092056248016278479853 79 (1) 1147240288157.26283825237209622143.197531251446059329471533015409 81 (1,3,9,27) 27767002339.37725805717350619429950429139147 83 (1) 167.499.17597.41580677.80781507941.605274844997.P25 85 (1,5,17) 26807981.20891158391.P32 87 (1,3,29) 2694217.1833921547.4706691035521.1357610070580129 89 (1) 8011.2064441331.P56 91 (1,7,13) 48215910563832798697.P37 93 (1,3,31) 186187.290869963.659988451.842660004553.1358539033057 95 (1,5,19) 571.1901.825838991.1298704628041.25425408247171.2995523312517361 97 (1) 389.1747.1586365166597.18969653181299397175271.P35 99 (1,3,9,11,33) 16633.18380539.18414001.226407819331.38167293140100433 101 (1) 1275678077.P69 103 (1) 2473.5563.160681.P68 105 (1,3,5,7,15,21,35) 211.35281.58171.P26 107 (1) 643.5044140393054571.P65 109 (1) 30726149494277.P71 111 (1,3,37) 89728627.187333846633.1487716834806007369.3561693323285489089 113 (1) 107351.54466954894479739.201436862864351419099.P46 115 (1,5,23) 461.1151.44851.257917526307345124973861.P35 117 (1,3,9,13,39) 6553.5958157609.39031258670353.P29 119 (1,7,17) 16661.29032062767.103198889691409.12405291558509977.P30 121 (1,11) 4163261521.1304380464883.P64 123 (1,3,41) 25512169.141304123.P47 125 (1,5,25) 5*.9536585501.117811792772681609501.105875321588567599765751.P25 127 (1) P99 129 (1,3,43) 43*.P64 131 (1) 263.3931.6551.1284827442574221936870974393373403.P59 133 (1,7,19) 11971.188861.1101773.164331230229374083.P52 135 (1,3,5,9,15,27,45) 175509721.P48 137 (1) 6577.25247731.53280671.60042056488501962187.P68 139 (1) 557.21407.128159.P96 141 (1,3,47) 283.13537.753554761.122320721569.989671414201.P33 143 (1,11,13) 859.62545486153056268832471.P68 145 (1,5,29) 132241.150433631394488258261.P62 147 (1,3,7,21,49) 32093041.P58 149 (1) 38538553.1318713554713829548602512956686040272376450743377909.P57 151 (1) 2623968964411.4956504421137000338429923175878885954098593563.P59 153 (1,3,9,17,51) 9757142011.12644443230579801886843521019.P37 155 (1,5,31) 3559267608341.208210289142572055121.P61 157 (1) 6446107.6423436771.81127299702871294523556776543. .8695994904356302134775281276601.P46 159 (1,3,53) 118721004139.67587459957091.P56 161 (1,7,23) 10949.593447.491787574454982121. .3358586137753609961516447641418203949.P39 163 (1) 653.2378523250342970947582043555610171717174452063.P78 165 (1,3,5,11,15,33,55) 331.13724862774476458441.P41 167 (1) 19466857.10301691259.229027359614687.9703107759710968661. .2200446540213260920441013.P55 169 (1,13) 677.3719.1420277.3066042413300025661761581713. .351082413599031251316269147227.P52 171 (1,3,9,19,57) 19*.25896916098621777025320461067950269867.P46 173 (1) 924669087985921.495043698717322221180325946047148316337.P81 175 (1,5,7,25,35) 3822701.114265201.141218351.7292423951.34840572551. .35107498301.2370825139201.P28 177 (1,3,59) 1421059369.P82 179 (1) 359.4297.399887.1126853766403. .171074041901536300021132517497157303.P80 181 (1) 39821.12684206910817829.P120 183 (1,3,61) 22335533202362157841587721.P68 185 (1,5,37) 1063053988637874955869001.P88 187 (1,11,17) 382229.4208612395681.6467774498519851224197542939036067237.P70 189 (1,3,7,9,21,27,63) 10644859.292645031213683.P63 191 (1) 383.120477626957.141173343133408897.172804791061171733536391399.P91 193 (1) 748132849.3759493321.230824001813.344929902064301. .577701497837906594854943.P82 195 (1,3,5,13,15,39,65) 523065274520717779891.795382366687653584971.P34 197 (1) 2235557.10123252906683101.P131 199 (1) 797.191837.3693839.484493690172684383. .2389106853487241752315685035579349880354989277451.P74 201 (1,3,67) 3196645037857.P91 203 (1,7,29) 1458188789.432549126887388039664858367.P95 205 (1,5,41) 66571969781.28852807210022072371.P95 207 (1,3,9,23,69) 399097.P98 209 (1,11,19) 18873119.414230477.84125065520563. .39547815403982363610457333838688241066157.P70 211 (1) 35768449921.127491843407.22502477360820492307768713607212049. .953864267757776424221068538656285528154532046177627.P57 213 (1,3,71) 22301660719710979.P93 215 (1,5,43) 1291.19660072438421.P115 217 (1,7,31) 385227416351.26316013765873042806112463084693. .1265855393578666785134496493194757776649681.P55 219 (1,3,73) 1143619.2820121693645487997956892799666256974847683.P64 221 (1,13,17) 4421.39721657.41183788762160210182927373892714194450477.P98 223 (1) 359734681.19261747635283.P151 225 (1,3,5,9,15,25,45,75) 320851.3388291201. .2056583697041569929017137051051.P49 227 (1) 1393781.141273137445779487073. .1994969355576066549710715311391607571195545033.P105 229 (1) 1505447.P172 231 (1,3,7,11,21,33,77) 174090854323.1526323866435523. .83531679812360869820818648177.P39 233 (1) 568465670186789.3945524703927668484254051089. .630076600824417505174717786052089.P106 235 (1,5,47) 941.88816955621.P130 237 (1,3,79) 15643.393024899619859590739537077043657.P85 239 (1) 479.555643125049.674693399227.2787187926109459.P144 241 (1) 248231.20481747682829.1840889044920084403. .7710038279791808580832936799. .246316726378395449466748758203811907753252397.P78 243 (1,3,9,27,81) 249844450267.47847655472636701140045116262913. .103939380360329666746292370686492281.P48 245 (1,5,7,35,49) 22541.P127 247 (1,13,19) 1483.77071411.329143658741.82569737524705024142782304189.P117 249 (1,3,83) 17929.63871987.30565451980162779163327091617.P87 251 (1) 503.34204273.59351200969.80440705758435499. C157 253 (1,11,23) 23*.1013.75168534000121. .259666046866989553234678839986188137176834471947.P106 255 (1,3,5,15,17,51,85) 1199699502336395787186091.P76 257 (1) 9767.17477.3309693452762216327. C173 259 (1,7,37) 2458852243. C159 261 (1,3,9,29,87) 523.467281506322297.1088767101178107721.P96 263 (1) 131982869. C196 265 (1,5,53) 1061.12721.59499149215409565615862915027061. .1443883079527663603943444340055791696913305571.P78 267 (1,3,89) 18530245891.P127 269 (1) 29083873645382611513.2334775781694290932919. .14914054997566758664316062644331821838847.P128 271 (1) P211 273 (1,3,7,13,21,39,91) 547.2430143818773217. .311093172628257376513996627655635721132089.P53 275 (1,5,11,25,55) 13751.10764601.1080416801397537451.P127 277 (1) 1109.5555507589053.152327217259127. .14011053856556766554595009793438946968040153039.C139 279 (1,3,9,31,93) 326892685378628881. .4195369622107561728725528588657828897923.P83 281 (1) 33721.186023.122413379955569789.228566796853368622765083206587.C162 283 (1) 36791.217516631.6650510037106913164557499908650923. C173 285 (1,3,5,15,19,57,95) 47562842881.270596289241. .209547179344816511252551051.P64 287 (1,7,41) 248848212837883.P173 289 (1,17) 671059.606329606788978761264759513146230361569.P168 291 (1,3,97) 111940600727841600317236399112257.P118 293 (1) 946391.193844113. C214 295 (1,5,59) 1181.19568032756311331.15208118255933834293359009545761871.P127 297 (1,3,9,11,27,33,99) 180794604080179.P126 299 (1,13,23) 599.5981.309379487.2341190333.394098064572643947287218201.C155 301 (1,7,43) 4941217.210619620359.387153001486618459. .1026218994621353041220001358738943323. .50018859578270750848409089664785836827007246435735770683387.P66 303 (1,3,101) 2529268867.4844162809.36536927761.257934717592273. .31140192590150713382146219858775467.P77 305 (1,5,61) 86011.2112242585382465957468782381. C155 307 (1) 1229.4762799.774471014077469888593.205898436168261867044624683.P182 309 (1,3,103) 619.P156 311 (1) 1191554036683.3666342101717.1028123934962242970067317. .7640150264100839651419559.C168 313 (1) 20032627.1280155603. C227 315 (1,3,5,7,9,15,21,35,45,63,105) 423123121.1076836800079531. .72725680608108905121706081.P63 317 (1) 15217.494521.P237 319 (1,11,29) 10847.642814987.105726751219.891967447801.22138289428735393. .1409088913314217103.50351395030858047251181629. .4528381576097816452461578808677.P92 321 (1,3,107) 24212302455882717029271553.3989017680658351355297802631081.P109 323 (1,17,19) 647.P222 325 (1,5,13,25,65) 1301.15601.903471092281594039875101. .9458999046244634687622911142066001. .570312905179987052421467082275470442757451.P80 327 (1,3,109) 2617.5233.16823497.161662095193.P143 329 (1,7,47) 13581753427437725779783140643. .5552584966550029192436491703687097023.C150 Table 6+ Factorizations of 6^n+1, n<=330 L,M for n = 12k-6<=654 n Prime Factors 1 7 2 37 3 (1) 31 4 1297 5 (1) 11.101 6 (2) L.M L 13 M 97 7 (1) 7*.29.197 8 17.98801 9 (1,3) 46441 10 (2) 241.6781 11 (1) 51828151 12 (4) 1678321 13 (1) 53.937.37571 14 (2) 421.5030761 15 (1,3,5) 1950271 16 353.1697.4709377 17 (1) 190537.12690943 18 (2,6L,6M) L.M L 73.541 M 55117 19 (1) 1787.48713705333 20 (4) 41.68754507401 21 (1,3,7) 2527867231 22 (2) 58477.70489.863017 23 (1) 113958101.990000731 24 (8) 5953.473896897 25 (1,5) 3655688315536801 26 (2) 313.2341.6291946695217 27 (1,3,9) 114967.883383463 28 (4) 281.337.617.81035189089 29 (1) 59.32713.2727192763388813 30 (2,10) L.M L (6L) 61.74161 M (6M) 181.3541 31 (1) 189491931189200021056951 32 2753.145601.19854979505843329 33 (1,3,11) 463.72073.127236649 34 (2) 934117.8289713345361373993 35 (1,5,7) 631.701.2311.9241.585131 36 (4,12) 577.3313.2478750186961 37 (1) 3923.1096762734443.2054788991719 38 (2) 1030762781149.9736145643041809 39 (1,3,13) 79.9049.868999.8857759 40 (8) 17761.3696985841.121206120881 41 (1) 83.28537.4837453663777044375040181 42 (2,14) L.M L (6M) 804146449 M (6L) 6055984789 43 (1) 412482688627178079807598675848631 44 (4) 89.150080764792922988676714149209 45 (1,3,5,9,15) 4760317816590150361 46 (2) 6073.2259889.9564781.128407494947883673 47 (1) 534577564460822791430647883899825591 48 (16) 193.8641.688490113.6931400449 49 (1,7) 7*.762332681442053.90179616936384011 50 (2,10) 343801.22243201.1748016735462726601 51 (1,3,17) 103.919.980146969.99617785207 52 (4) 192193.14090441.8284434950526240125727017 53 (1) 107.97351567.33685364386033.71080464397105403 54 (2,6L,6M,18L,18M) L.M L 591841.171467713 M 109.932461936453 55 (1,5,11) 11*.1031141.16336066781.84155540944421 56 (8) 113.4817.4048129.10189440239012883075423169 57 (1,3,19) 457.137713.190324492938225748951 58 (2) 349.105134528469779071670501631159328247729809 59 (1) 1163658999540220416412446482708919139658591671 60 (4,12,20) 13441.592575109627400042641 61 (1) 9151.4577830180684945360162613198286645069141001 62 (2) 47552767764994953232854569779888803761183529901 63 (1,3,7,9,21) 127.154260982009.528921402377887 64 4926056449.447183309836853377.28753787197056661026689 65 (1,5,13) 131.199930782298483523040584108028862541 66 (2,22) L.M L (6M) 3037.96493.4629769 M (6L) 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C191 275 (1,5,11,25,55) 11551.1458601.541019051.P137 276 (4,12,92) 100600260657132106393367429005921.P105 277 (1) 8311.9419.113017.8065133.143476139909.P184 278 (2) 1561232989.P206 279 (1,3,9,31,93) P141 280 (8,40,56) 3361.275521.11672641.5576968321.P124 281 (1) 563.8431.1351757950997.14063062521302839553357. .19974696199623424031237.115600460578650720383010805853.P126 282 (2,94) L.M L (6L) 3337903223042569.P57 M (6M) 9491602000279600777.P53 283 (1) 2229970063115387665250948239. C193 284 (4) 569.392489.469077689.896041468925733187137365896107353. C168 285 (1,3,5,15,19,57,95) 40844746349999464436020322521.P84 286 (2,22,26) 252253.29518633. C174 287 (1,7,41) 1121023.2853115756372329930021879179. C154 288 (32,96) 1153.1984301569.1567103187499033148929.P116 289 (1,17) 8093.23278892925034258318294404644503. .7679962361209350795245766079339091.C143 290 (2,10,58) 1741.375841.P166 291 (1,3,97) 135607.3343385035897.P132 292 (4) C225 293 (1) 587.17828792392643.P212 294 (2,14,98) L.M L (6L,42M) 8434052750068597.P50 M (6M,42L) P66 295 (1,5,59) 20441552166028072811.P162 296 (8) 593.137045594113.6758410568257.55197682698737. .8375829463350094657.45637046233441330193. .2829247728806215136257.147071192694046077687504556871041.P92 297 (1,3,9,11,27,33,99) 2377.4159.50147190436375827433.P114 298 (2) 6825688699471381. C215 299 (1,13,23) 3241759.5666051.P193 300 (4,12,20,60,100) 2056871500653135843616345033288599993601.P86 301 (1,7,43) 298183187219.393091150299531749364205297712116979. C150 302 (2) 19515241.8951289532327540357.27564163622315314490824935535295293.C173 303 (1,3,101) 10303.21561481. C145 304 (16) 440123297. C216 305 (1,5,61) 10542843898331.P174 306 (2,6L,6M,34,102L,102M) L.M L (18M) 613.12241.846370054558596518376711409.P41 M (18L) 6121.57372656104261.P58 307 (1) 4732562084333249714196514227673.55385698371129588030629087875349.P176 308 (4,28,44) 65725969.59649652128793520533433.P157 309 (1,3,103) 427039.26432479.P146 310 (2,10,62) 27901.50221.372201769081.56112296349610045406881.P144 311 (1) 25253560139.4310758347899.18707517257089. .65268623352510374655683719.15375997422186291719933915126668351. .2495174740032337104455007012996408231601. .3864978146331181248248106309395051058288828336437.P57 312 (8,24,104) 1249.94578317595841.P133 313 (1) 2269959032465874003365857.P219 314 (2) 558436298701.43877671534791092362933. C209 315 (1,3,5,7,9,15,21,35,45,63,105) 2725667472495241. .8813032387117882454692315491751.P66 316 (4) 1578867457.16162944961.88362484215497. C210 317 (1) 974459.4340223635815993. C225 318 (2,106) L.M L (6L) 40133011425325338673.P62 M (6M) 6997.10786528430680870971861642463992861493.P40 319 (1,11,29) 1277.169709.1034019361.1252217116623387773.P183 320 (64) 641.6827521.621432697463041.1743036582663429761. .2480431288764419201.P139 321 (1,3,107) 2651847769.P156 322 (2,14,46) 1933.2593505209.4762756207579441.P178 323 (1,17,19) 13567. C221 324 (4,12,36,108) 2593.3889.40567195306213128342900074449.P133 325 (1,5,13,25,65) 43798301.88461995051. .512517661513971729536179593061506405316951.P127 326 (2) 9128653.862123028232465233166133318203195759014737. C204 327 (1,3,109) 32560222715988756820062781110511873.P134 328 (8) 554977.1487809.P238 329 (1,7,47) 659.6581.131589345007.29091932006593.6417221204788802521. .99379633714344941623.560877906720787934003619587. .688032426812647379990413979.P92 330 (2,10,22,110) L.M L (6M,30M,66L) 661.144541.14966414761.P45 M (6L,30L,66M) 1321.110221.188074921.P46 ------------------------------------------------------------------------------- 342 (2,6L,6M,38,114L,114M) L.M L (18L) 60204997.4765941001.235011794248567117.473164737913969822009.P29 M (18M) 37187713.P77 354 (2,118) L.M L (6M) 709.2833.254923189.P76 M (6L) P91 366 (2,122) L.M L (6M) 8053.241561.10161211191529.457346879849878822260409.P47 M (6L) 733.3069462805228338593646133.173941000965538537755852657517.P38 378 (2,6L,6M,14,18L,18M,42L,42M,126L,126M) L.M L (54M) 10794083454463066294342208029552733580361.P45 M (54L) 757.9829.2592266236335984818021237855668549.P44 390 (2,10,26,130) L.M L (6M,30M,78L) 342421.55088625341568479584667598703368001.P35 M (6L,30L,78M) 1222106886101401.P60 402 (2,134) L.M L (6L) 1609.18493.6400916741826776608939188781.P68 M (6M) 98266387530667777.P86 414 (2,6L,6M,46,138L,138M) L.M L (18L) 1657.102673.284833.31739306955000318682004605762105132924971289.P46 M (18M) 829.11959280174921358157113444778096591384713470257.P54 426 (2,142) L.M L (6L) 853.99535753.15006883477.17403644677. .1092776175604936226930157745921.P48 M (6M) 17041.5123509669.61803564541.253055139049.P73 438 (2,146) L.M L (6L) 1753.26245837.51911357917.3329634082406617. .4322128701610242421.6898119095402110707133.P36 M (6M) 8761.283480200282934561.P91 450 (2,6L,6M,10,30L,30M,50,150L,150M) L.M L (18L,90L) 26922319201.P83 M (18M,90M) 5771844901.15198535801.2724303865501.312241283985799801.P44 462 (2,14,22,154) L.M L (6L,42M,66M) 7393.55441.449989.2123353.3834601. .447309338300844744160129.P43 M (6M,42L,66L) 938733964477.46094532937993.81154591004568313.P52 474 (2,158) L.M L (6M) 3793.P118 M (6L) 5689.18709729.317233981.1945096921.P94 486 (2,6L,6M,18L,18M,54L,54M,162L,162M) L.M L 763296049.P118 M 170827321094639893.3409463117689442128783261. .31714835472740596249852635626281791475129.P44 498 (2,166) L.M L (6M) P128 M (6L) 1993.245351666247788560312408234856037538218169.P84 510 (2,10,34,170) L.M L (6M,30M,102L) 484601490571886903493518015104501.P68 M (6L,30L,102M) P100 522 (2,6L,6M,58,174L,174M) L.M L (18L) 2089.290924056117.947349493773774517.P99 M (18M) 359137.2797958656485541.P110 534 (2,178) L.M L (6M) 1069.694201.28031381649109.196947355253345341.P97 M (6L) 2137.723739848857641030189.P114 546 (2,14,26,182) L.M L (6L,42M,78M) 15289.P108 M (6M,42L,78L) 16381.1627627815399713377343163471649631733474853.P67 558 (2,6L,6M,62,186L,186M) L.M L (18M) 11161.157462752204253.21124214217163783261. .1520168756245321923557857.P79 M (18L) 1117.P138 570 (2,10,38,190) L.M L (6L,30L,114L) 2281.2358661.3817262181721.6197208621830041. .888066870806284147801.P53 M (6M,30M,114M) 18805516694127001.P97 582 (2,194) L.M L (6L) 1696995935981617.P135 M (6M) 97*. .1083115891949143826648635366282163052400438187303499464609499226261.P81 594 (2,6L,6M,18L,18M,22,66L,66M,198L,198M) L.M L (54M) 28964629.15536649073902661.29426749337349541. .19429747183583833735981.P78 M (54L) 3155329.17698960601683054308649.3512830966112683782744191389.P84 606 (2,202) L.M L (6L) 1213.25453.215737.930985424669173.P129 M (6M) 3637.181339441.73805592037.257309257577257.343320968801689.P104 618 (2,206) L.M L (6M) 33703023049.31712196448668781.P132 M (6L) 1237.33479895313601650365695117603613865333.P119 630 (2,6L,6M,10,14,30L,30M,42L,42M,70,210L,210M) L.M L (18M,90M,126L) 514379712421.9226830539692081. .2531978618650256393162606524681.P55 M (18L,90L,126M) 2521.6797701.34640925953158940597772893101.P74 642 (2,214) L.M L (6M) 5972962561.1426969200507388358761.1740269104463086681404229. .10200602444075618255654001255237011614621.P70 M (6L) 10273.533550328536694908746148449547022477.P126 654 (2,218) L.M L (6M) 132109.878550901.70971053221.7163969211901657. .151876907354130504916630163154066721. .1480112921488586442378283240412840195548801.P50 M (6L) C169 6^{6h}+1=(6^{2h}+1)L.M, L=T^2-T.6^k+6^h, M=T^2+T.6^k+6^h, T=6^h+1, h=2k-1. Table 7- Factorizations of 7^n-1, n odd, n<300 n Prime Factors 1 2.3 3 (1) 3*.19 5 (1) 2801 7 (1) 29.4733 9 (1,3) 3*.37.1063 11 (1) 1123.293459 13 (1) 16148168401 15 (1,3,5) 31.159871 17 (1) 14009.2767631689 19 (1) 419.4534166740403 21 (1,3,7) 11898664849 23 (1) 47.3083.31479823396757 25 (1,5) 2551.31280679788951 27 (1,3,9) 3*.109.811.2377.2583253 29 (1) 59.127540261.71316922984999 31 (1) 311.21143.3999088279399464409 33 (1,3,11) 3631.1532917.12323587 35 (1,5,7) 2127431041.77192844961 37 (1) 223.2887.4805345109492315767981401 39 (1,3,13) 486643.7524739.44975113 41 (1) 83.20515909.4362139336229068656094783 43 (1) 166003607842448777.2192537062271178641 45 (1,3,5,9,15) 1527007411.125096112091 47 (1) 13722816749522711.63681511996418550459487 49 (1,7) 3529.1074473.13473433.6106505825833677713 51 (1,3,17) 103.365773.2316281689.10879733611 53 (1) 8269.319591.38904276017035188056372051839841219 55 (1,5,11) 5457586804596062091175455674392801 57 (1,3,19) 19*.19609.879399649.6957533874046531 59 (1) 459257.134927809.550413361.354639323684545612988577649 61 (1) 367.4759.177237331.1914662449813727660680530326064591907 63 (1,3,7,9,21) 2643999917660728787808396988849 65 (1,5,13) 131.157951.787021.4446437759531.434502978835771 67 (1) 228337.147300841.206244761.10052011757370829033540932021825161 69 (1,3,23) 139.402011881627.235169662395069356312233 71 (1) 990643452963163.169002145064468556765676975247413756542145739 73 (1) 439.3675989.359390389.1958423494433591.7222605228105536202757606969 75 (1,3,5,15,25) 29251.217648180992721729506406538251 77 (1,7,11) 724487149.6809710909.88262612316754526107621113329689 79 (1) 913242407367610843676812931.1056836588644853738704557482552056406147 81 (1,3,9,27) 3*.1621.3727.3368791.70722308812401674174993533367023 83 (1) 167.66733.76066181.7685542369.62911130477521.303567967057423. .18624275418445601 85 (1,5,17) 1531.4931.P48 87 (1,3,29) 2576743207.196915704073465747.358475907408445923469 89 (1) 1805633.18489605314740987765913.P46 91 (1,7,13) 7304123737.231410451435538144122809.P28 93 (1,3,31) 5463751.2211164386353499.P29 95 (1,5,19) 36671.1966385431.P47 97 (1) 389.971.P76 99 (1,3,9,11,33) 199.173647.P44 101 (1) 607.809.6263.P76 103 (1) 17923.P83 105 (1,3,5,7,15,21,35) P41 107 (1) 227109283745807808529.1620221568881364582821.P49 109 (1) 14551288401737861.63505707690048880101785428103.P47 111 (1,3,37) 6217.177379.56713875643149053038693.P29 113 (1) 227.P93 115 (1,5,23) 1151.188831.1446701.723461377501.27229507836853201541.P29 117 (1,3,9,13,39) 1873.322921.2280097.7687225261.P36 119 (1,7,17) 12377.34273.305213588009240737.440779823883628367834893.P32 121 (1,11) 1453.65099.11795261559086963.58792315124013823398811997.P44 123 (1,3,41) 267403.P63 125 (1,5,25) 251.2182816753758823696751.P61 127 (1) 260461507.554351226505275380676162672703.P69 129 (1,3,43) 10837.63350976270733.175446584281395198837259.P30 131 (1) P110 133 (1,7,19) 401563177.2662276961.373740808373213.897558513407803666357.P38 135 (1,3,5,9,15,27,45) 271.185221.175561876921802311.P36 137 (1) 2741.213721.251533.57162922399254002352124124899. .65480203458464902965944539043.P44 139 (1) 19739.673039.P107 141 (1,3,47) 283.5960917.P69 143 (1,11,13) 528808508322667.376215890379315997311416372784691746214777.P46 145 (1,5,29) 4899841.277463632645667965008782910911.P59 147 (1,3,7,21,49) 4060603391041.424770871339903301567509.P35 149 (1) P126 151 (1) 115356256117.36076003832567.206462520503013793561. .2856349001315592319937.P61 153 (1,3,9,17,51) 307.613.4591.44371.44072862804091655188147.P45 155 (1,5,31) 21391.21701.1622982371.9254997611.P74 157 (1) 4397.5653.1039945344901.P113 159 (1,3,53) 32119.1695259.84247682063005850464952755729.P49 161 (1,7,23) 4406588677.4615185796935334098258901.P78 163 (1) 653.9781.1260643.962207945014470392304193. .1648536343690282975764489383562678396141955057.P55 165 (1,3,5,11,15,33,55) 7591.36647640811.1946951063386221338821.P32 167 (1) 2158061509.623932374204290945359. .494816894793945434195756741367539.P78 169 (1,13) 1452979915402500135854417362573926368874134931212567.P81 171 (1,3,9,19,57) 18684829.9674698906207.175336938770236118176950803989.P42 173 (1) 9491935586594867440367391646466925926211879363793.P97 175 (1,5,7,25,35) 701.1237578612719152201.1094471317606762277701.P60 177 (1,3,59) 709.89209.22724865586634953261986967832791.P59 179 (1) 41887.149874987000926513705179.P123 181 (1) 1811.13873726021.618805947190964867.364308807786322943430987769.P95 183 (1,3,61) 5153013553.104199666470736545959920137256413473.P57 185 (1,5,37) 1481.6661.219041.P110 187 (1,11,17) 10099.107969286569. .157663427378398137465490451049503570558624435143.P73 189 (1,3,7,9,21,27,63) 757.5906255349477660375285361.P64 191 (1) 383.35546396841548971517329.P136 193 (1) 14669.85728285355409267895679.756937155910390044916932629. .5994946327304712468705571873826831. .4539546970485536436424707475812653713.P38 195 (1,3,5,13,15,39,65) 567538141.14046059431.P63 197 (1) 3547.6159369299.P153 199 (1) 3583.214661295139431885643832154153997. .86539116653269014086961051020627012232284504261471.P82 201 (1,3,67) 85627.132955527487.775594571863.98527557194917. .428995274049217.P55 203 (1,7,29) 29*.60089.145916619612283783386370190568409. .1158560595990812530792619356788467777477674946730941.P53 205 (1,5,41) 834035491628067397615971778938263976927180494349982302975033997201.P70 207 (1,3,9,23,69) 77569456660417.227556220136287506028942276770826968937.P60 209 (1,11,19) 8048541876545647951.P134 211 (1) 141793.259018281812228908974285857741797668601708632994386\ 95413795254930505191880636307.P93 213 (1,3,71) 968299.582053568181. .1274759667849259732505774376326193816317726317.P56 215 (1,5,43) 31391.822161.11300176322829911971.147795410845880963171. .11916717598664539151308306888803765941891.P53 217 (1,7,31) 604997.1956808820481173.602858801824822604293. .626475940065539137153553.14784849807251837047947491359227676537.P50 219 (1,3,73) 877.16999040225222266951.P100 221 (1,13,17) 22543.760999500977.9761302041992117524910703947100342853.P109 223 (1) 17288166877.132218621369.P167 225 (1,3,5,9,15,25,45,75) 8101.1708445701.121257418374086998051. .20297781182169478546946347835701.P37 227 (1) C192 229 (1) 50839.8771561006313491618219260558398401.P155 231 (1,3,7,11,21,33,77) 1793870233.125844538662442909. .3752691545947560669458268649.P48 233 (1) 467.79227874003.13514998546886646078035233993. C155 235 (1,5,47) 2812894619735804087343816418261851587705080375647708714001.P98 237 (1,3,79) 2371.529637338334729405483135077873.P99 239 (1) 479.871986721.643384173113837.4040609273925388685799856703093687.P142 241 (1) 1447.28439.33486078253526557.580351872045743557. .547283138069536869412948975377385222182769003. .2937026550451562627666151150279078330125909163812627.P65 243 (1,3,9,27,81) 3*.1459.169129.1382671.73870787476849933393474604683663.P91 245 (1,5,7,35,49) 4896864001.9152363081.11492120512321. .353207957997402826578121.P86 247 (1,13,19) 6917.22931541257.14975869588530371.P153 249 (1,3,83) 11606389.41491794184631137. .76354359945860977734571491962874304923412180177.P68 251 (1) 503.27611.8895962998159.P192 253 (1,11,23) 1106436299. C177 255 (1,3,5,15,17,51,85) 580381.326568900271.604822302841.P80 257 (1) 1543.1998784090958019204289. C192 259 (1,7,37) 3109.65269. C175 261 (1,3,9,29,87) 523.5743.83226515419.710074092185677. .474062506708242760701771553376690953.P75 263 (1) 111473077.246420328513. C203 265 (1,5,53) 1061.3041671.19069931.187978422699271372501. .212135996587857465774994583472077008056991. .105322961980986497356836647823085697438251004501.P51 267 (1,3,89) 28713855773905923529325586129605726947029936343189321\ 74130446555537271.P80 269 (1) 2153. C224 271 (1) 6780421.164514887. C214 273 (1,3,7,13,21,39,91) 1093. .894265285117657047082911243254861366638596090445735393.P65 275 (1,5,11,25,55) 2429297864813474051. .13108478445679585187945846562792720732451. .152254207931524870640907264181257222395351.P70 277 (1) 137947.8954857.607705768105925529871. C201 279 (1,3,9,31,93) 8248454734032306396350042707176588234070405742014804291507291.P92 281 (1) 563.8431.341614931501.4420135738596254569. .372634096091628229321039358180848549.C165 283 (1) 644316289.182739497717749501.P213 285 (1,3,5,15,19,57,95) 523261.93586760776923620671. .80183934664292567561851.P74 287 (1,7,41) 12412177.2405532607493.21747676457911610417. .738710854664932373205737588298090279327121.P123 289 (1,17) 1828793.801172436655296029591646500403317187. C188 291 (1,3,97) 4657.134002009.951340693.23363930803. .588884936839088389773662393029.11089767531884977816638380462821.P71 293 (1) 587.15823.P240 295 (1,5,59) 123311. C191 297 (1,3,9,11,27,33,99) 5347.27170749.P141 299 (1,13,23) 1045903.5240570609.64432450872271. .124017815182557414772494313985201. .121219249940833404770079915022116301.P127 Table 7+ Factorizations of 7^n+1, n<=301 L,M for n = 14k-7<=595 n Prime Factors 1 2.2.2 2 2*.5.5 3 (1) 43 4 2*.1201 5 (1) 11.191 6 (2) 13.181 7 (1) L.M L 113 M 911 8 2*.17.169553 9 (1,3) 117307 10 (2) 5*.281.4021 11 (1) 23.10746341 12 (4) 73.193.409 13 (1) 53.228511817 14 (2) 13564461457 15 (1,3,5) 6568801 16 2*.353.47072139617 17 (1) 29078814248401 18 (2,6) 13841169553 19 (1) 351121.4058036683 20 (4) 41.810221830361 21 (1,3) L.M L (7L) 309079 M (7M) 51031 22 (2) 661.1409.83960385389 23 (1) 3421093417510114543 24 (8) 33232924804801 25 (1,5) 79787519018560501 26 (2) 157.1195857367853217109 27 (1,3,9) 1628413557556843 28 (4) 337.2129.517553.515717329 29 (1) 402488219476647465854701 30 (2,6,10) 61.555915824341 31 (1) 373.9754399.5420506947192709 32 2*.7699649.134818753.531968664833 33 (1,3,11) 67.1357105535093947 34 (2) 137.59361349.133088039373662309 35 (1,5) L.M L (7M) 421.12128131 M (7L) 71.603926681 36 (4,12) 42409.137089.32952799801 37 (1) 149.15572244900182528777225808449 38 (2) 2598696228942460402343442913969 39 (1,3,13) 79.23850061.115868130379 40 (8) 881.542081.2312581841562813841 41 (1) 4849399.8999993.1636258751.78009515593 42 (2,6,14) 195489390796456327201 43 (1) 947.19867.20899.163573.235211.3799051.4749781 44 (4) 89.8713.8206973609150536446402438593 45 (1,3,5,9,15) 541.154351.295831.7777981 46 (2) 26681.649981.15513961.55681942361860463813 47 (1) 655417289594537954307682339857743931943 48 (16) 97.104837857.108604397663266369 49 (1,7L,7M) L.M L 197.883.161309.19847549 M 3823.1445599.101361401 50 (2,10) 5*.101.13001.25301.38327966300231909291101 51 (1,3,17) 1135261.12192877.90920746649833 52 (4) 313.85094881.1377454635342537460935008154217 53 (1) 107.345449549.35416476134069.58902316970027001503 54 (2,6,18) 26893.167039577217.590297313273013 55 (1,5,11) 11*.331.2311.38501.2864401.7840815905526451 56 (8) 449.673.39648001.21535258550401.142256806230113 57 (1,3,19) 457.24006520939.275430251632699963 58 (2) 233.136853089.55716067510309.116714640028973541741413 59 (1) 122131.4261190159.1187164242679.14683403662888806475673 60 (4,12,20) 12913561.85560261859655897641 61 (1) 444519128147170444656914672945689439050880209231501 62 (2) 33947629297.74502648768583254173.196846325409292090901 63 (1,3,9) L.M L (7L,21L) 127.9829.1506625093 M (7M,21M) 20801593.67979647 64 2*.35969.1110623386241.15266848196793556098085000332888634369 65 (1,5,13) 1175071.35695043869049049222174543845808031 66 (2,6,22) 29569.2784937.678240817.116320403133001 67 (1) 20771.6557750853567755279.383942665465635068312581125821527 68 (4) 20129.94793.638991748543082113037456009420293477766438233 69 (1,3,23) 277.7396787205469.8501948915136155490673 70 (2,10,14) 102314938321.18690488255321.19584845505919961 71 (1) 1351405472411521.92914860840816888117372433724419584467881183 72 (8,24) 129169.25726609.51385969.635311009.338325042961 73 (1) 3067.279883.7167647480643504302058174754486698790538818746798241 74 (2) 6891042949305882214394659726647344864958515967158596120016737 75 (1,3,5,15,25) 151.6005492312551.7021370289199888801 76 (4) 44118001.700197881.1295161807633.1299254811081649.135214434686939513 77 (1,11) L.M L (7M) 258576319.32817262777539703 M (7L) 463.333103.443632323630099913 78 (2,6,26) 13*.365302616611175569.7886422107556319674933 79 (1) 317.2874811.7573763065938754357.P39 80 (16) 38470561.102118777045028801.P30 81 (1,3,9,27) 163.487.15877.P37 82 (2) 33842057.5449628176194898649.P42 83 (1) 6963362191.P60 84 (4,12,28) 3361.4894546210513.2232059760329037670187857 85 (1,5,17) 1590988506392861.P39 86 (2) 173.1033.P66 87 (1,3,29) 5406066031.1284564941030772067.34720058992462423813 88 (8) 2085729338353.P56 89 (1) 179.3917.18691.1179536907057197599849.P44 90 (2,6,10,18,30) 9901.1795168434777002101.2065025164427492401 91 (1,13) L.M L (7M) 732700162559.1362621396812563889 M (7L) 467280997.17225454456724489912483 92 (4) 1657.197202518881.1812487089636161.P45 93 (1,3,31) 149731.P46 94 (2) 95881.4574857237.P64 95 (1,5,19) 571.1765151799417091.2440590160473742205021.P22 96 (32) 2113.9917569.596878081.16356157057.5962150442139230211450049 97 (1) 599599487.146533138940077.P59 98 (2,14) 16073.1933665951863017.10148051647066664017.P33 99 (1,3,9,11,33) 8095532743.244188888967.P30 100 (4,20) 401.P66 101 (1) 230281.3843253.P73 102 (2,6,34) 2857.85647973.P43 103 (1) 1031.490201721.1058638292629.461785968654529. .41875773535891952971477.P26 104 (8) 17712988461899423081645348353.P53 105 (1,3,5,15) L.M L (7M,21M,35L) 450798894542150330401 M (7L,21L,35M) 211.338640865331157691 106 (2) 15053.7627549.P77 107 (1) 1499.82413922847.P76 108 (4,12,36) 40177.60922880584567163834041.P34 109 (1) 5233.10059414761347582747.P69 110 (2,10,22) 2861.32561.543841.47045037529563701.P38 111 (1,3,37) 15015834247.25443079695091.12558090335903767.P22 112 (16) P82 113 (1) 1583.8654522423.120249742857138175784797627. .4842723074886320121848080733.P28 114 (2,6,38) 229.P59 115 (1,5,23) 1207501.100429501.P61 116 (4) 14153.769756513.33510280238484636857761.5192033853710499967501529.P35 117 (1,3,9,13,39) 1171.1174681.5075833207537.882351727670323.P25 118 (2) 149153.165437.1024477.6551912456787047841933817.P57 119 (1,17) L.M L (7M) 953.377231.20123377.1910207075448557917128553 M (7L) 239.2381.973897.P30 120 (8,24,40) 241.5789644155060072001.P33 121 (1,11) 26863.2174310226212366107469266007290639.P56 122 (2) 4497653.133440673.369232401898464835382701047039367301441.P49 123 (1,3,41) 395617447.P60 124 (4) 4217.2541312025433.23235518871793.P73 125 (1,5,25) 751.1173001.4833574921448501.31818863467130251.P44 126 (2,6,14,18,42) 1009.250993.2304793.31864919689.P36 127 (1) 35852863.P99 128 2*.257.769.197231873.6856531741041792239054980342217258517995521.P52 129 (1,3,43) 43*.1857499496101.499711620081214598029911373.P31 130 (2,10,26) 134358901.P74 131 (1) 263.86461.1686923681.P94 132 (4,12,44) 1321.532489.98138029441.P48 133 (1,19) L.M L (7L) 254997629797.265043186297.193935377097018854700131 M (7M) 8513.P42 134 (2) 269.3217.4591913.39144122221793.27982218262152281.P69 135 (1,3,5,9,15,27,45) 40724371.17796529171.P43 136 (8) 17*.5388077170097.49853897949169.P81 137 (1) 28771.893081081.7448353120289.P89 138 (2,6,46) 829.21529.26497.5755716973.153943464633957793.P36 139 (1) 557.5312442648966139012589.190705279598948669274660288301207361.P57 140 (4,20,28) P82 141 (1,3,47) 7333.P74 142 (2) 569.853.29537.810253.40109647514545875958117.P80 143 (1,11,13) 108109.145861.2547984152429.36383445305923.P66 144 (16,48) P82 145 (1,5,29) 227327521.P87 146 (2) 293.20149.36793.729810133110395035429089427259624129.P75 147 (1,3,7L,7M,21L,21M) L.M L (49L) 10157701.10738939.2868318061062142721089 M (49M) P36 148 (4) P122 149 (1) 10133.47338433355189929279110650931837806119829008573928501623.P66 150 (2,6,10,30,50) 5666701.169293601.1149016121562093219301.P32 151 (1) 1014952541.P118 152 (8) 12161.34961.72353.P109 153 (1,3,9,17,51) 56611.734707.469022340889.9035330762005111.P43 154 (2,14,22) 617.5302529.4181043906823655873. .152111801516025381573834946322977.P42 155 (1,5,31) 5581.60761.6689491.136823162401.92105555489371. .18127525360389024220391.P39 156 (4,12,52) 8737.45553.P73 157 (1) 57149.538511.3065983647843013.6053210945000213. .1296120348255709333595477995627.P60 158 (2) 13059374383501.24911171121703051981.40157473329867190572836333.P74 159 (1,3,53) 305033517629290547304139.3475913288653967871883271299609.P34 160 (32) 641.163344191041.4821999754197347683089799168482241.P61 161 (1,23) L.M L (7M) 49613117.8884810040009.P35 M (7L) 1289.P54 162 (2,6,18,54) 33049.52813.6115477804490161.P67 163 (1) 99640870978732398443. .5073984584534267042701366192312558139347152929.P72 164 (4) 141375169696201183349885463641977.P104 165 (1,3,5,11,15,33,55) 951113761291.83723745489451.539555593782065191.P24 166 (2) P139 167 (1) 84609883.18840106986299.819417374559877.P105 168 (8,24,56) 121633.334224081623006401.8636794070026393288992369697.P31 169 (1,13) 46307.39899177220516741740469143831233.P96 170 (2,10,34) 1021.15425560249042501.26072363006406325854739861.P64 171 (1,3,9,19,57) 2053.6841.538309.74560887186814269973. .3805658347924925639235001.P34 172 (4) 9127292833.1240400287144237937. .384756252551799653157355170166535055814550369.P70 173 (1) 347.2423.50344039.471539527. .153070037700933331054524248476494792173.P85 174 (2,6,58) 349.77216590050964983143652251131561.P61 175 (1,5,25) L.M L (7L,35M) 3851.8230203760252601.P32 M (7M,35L) P51 176 (16) P136 177 (1,3,59) 82483.30308419.1463159201029.P74 178 (2) 2137. .6670001035767378656954255161929184701347978922160475516532776621.P82 179 (1) 359.5227541273369.191499930339009469.484537357606024275557. .97776360820654218154951.19818717012982215688309021529.P46 180 (4,12,20,36,60) 93273670767719119849201.P59 181 (1) 1087.3259.869887.41293569401198114715784283. .222115594362913033859606616935084264949119264129.P67 182 (2,14,26) 4208753465884607397726922333124602824618429719033.P74 183 (1,3,61) 22308770410847159047.P83 184 (8) 184369.6291093953.293615126959601.4961889461604693798857328257.P92 185 (1,5,37) 325852711.637267603891620815515472232790301. .1803380635085187494461189037326621.P48 186 (2,6,62) 1861.405148344889.60515949735938678857.P67 187 (1,11,17) 1871.7119993477462624445303.P111 188 (4) 326369.650909936062481571307414656986709933264881.P109 189 (1,3,9,27) L.M L (7L,21L,63L) 379.75736555536290042899.150497847036363835206199 M (7M,21M,63M) 198829.415801.30584009107.1707078974907610627202377 190 (2,10,38) 2617061.110943661.2250656021.3050589519086201. .45065286561682421139793282921.P54 191 (1) 1896349613. .31965885239172324178492996736290000958581033942895383913544482645687.P84 192 (64) 1153.55681.12644353.2474441815297.3020677481177462138881.P60 193 (1) 7542501761.64335170279671. .5023922419530075554880849680462185748909.P99 194 (2) 79153.11695740049349.101761712426028087493813409017. .5682612984161495984352311495269241.P82 195 (1,3,5,13,15,39,65) 1232401.118177021.P67 196 (4,28) 68993.500977.P132 197 (1) 7246911739.P156 198 (2,6,18,22,66) 397.257401.246830400797725347589009.P71 199 (1) 4588543.34266607.P154 200 (8,40) 210127601.14462056001.283231036001.P106 201 (1,3,67) 1475302430815774454593471971258812767057737919471.P64 202 (2) 11717.32844797.P158 203 (1,29) L.M L (7L) P72 M (7M) 699539.10931551.252777631.640915395596561.P35 204 (4,12,68) 2852622546217.14736450261056323705201.P74 205 (1,5,41) 821.982435845672451.P118 206 (2) 3709.51913.115361.38774969.122087137.28702255943293301. .24643851880680753997.85260663016194334109048149.P82 207 (1,3,9,23,69) 1200187.5394493693.43363095901832281006261. .46987948541428377962695535792142217.P39 208 (16) 41237249.905547932264861071666229565143230129859275489.P110 209 (1,11,19) 2927.326589253.2953667228251580029339756726838729574091.P101 210 (2,6,10,14,30,42,70) 5981641.147388921.P67 211 (1) 255571219.986018415638331144897705149152887163110839. .1782698571759822944425464521670215514283481531471069.P76 212 (4) 29930161.P169 213 (1,3,71) 2358779222910769.5163412518685933. .1886450423022355815248392428881107832527.P49 214 (2) 5606801.13864445393.4170493266061. C150 215 (1,5,43) 431.41281.4674932375366381.13470457618790060895951151. .40183448134459496127723158417549037223081.P54 216 (8,24,72) 433.2161.19009.455761. .193509085665339680074571429441497198565924689.P62 217 (1,31) L.M L (7L) 25638551.10471226501.3880053969769335736807493.P35 M (7M) 1048084151605026323873056941440759.P43 218 (2) 133417.1689506462393.1183634452833113.15902619513553141. .198558877793513066390969.1854413147145016784219270865881. .3316547850397693557131427838097992150273.P41 219 (1,3,73) 329021320690441177.P105 220 (4,20,44) 3153774361.7018271947721.66582594292663681. .34347664112526074866442921.P71 221 (1,13,17) 443.1327.65312573.588631616197.P137 222 (2,6,74) 28063132333.110960237137.129405102503301790657.P81 223 (1) 20071.210020081728371166287199953172049233. .14552020391616867751861787376003405019.P111 224 (32) 45697.2425413779895399260276908118509697. .344893183164325811790731098404717953.P89 225 (1,3,5,9,15,25,45,75) 1801.142845016408087602151. .1083803739493312667701.P57 226 (2) 1702570097.2678163373711493257558608239592337.P147 227 (1) 229035283.154282766133562846357.709711268528327341336958053319.P133 228 (4,12,76) P122 229 (1) 13301829773559449929333573.1786097907260768050299030591589751. .5560213957904401146976358164020003882623.P95 230 (2,10,46) 461.48203401.1853224081.9118947413041. .996024428653721875791186905187314201.P81 231 (1,3,11,33) L.M L (7M,21M,77L) 8317.207734163253.9508049868703.71301115589607904751983 M (7L,21L,77M) 6007.13399.4612609.P36 232 (8) 2101854113.2138683649. C171 233 (1) 179411.9017101.54708069359245754606781357934918261. C150 234 (2,6,18,26,78) 445069217792093194807364989.P96 235 (1,5,47) 77081.10943951.2963635864903802720551341744191. .3526044283547082417510281214088597814021244392943907181.P59 236 (4) 143400661121.17543686562323601.187381402716244523401. .72365309203156796180466302654219233. .820897392402727154889937592766080854712048479741649.P63 237 (1,3,79) 1423.4094413.90359966617569667185245947327.P94 238 (2,14,34) 234193.4734058001.110453935177797989849. .10947514021187304312714127746617.P97 239 (1) 3347.55927.123803.708841389407. C176 240 (16,48,80) 8442444961.P99 241 (1) 148457.90728789.185733701631563.620299344228439. .7301646764233669.667245220429235891.187553380824058857638969.P104 242 (2,22) 13553.9458403989.533717102782679769299809.P149 243 (1,3,9,27,81) 104491.254984917951.134564057912629.P107 244 (4) 977.2441.1424727548622109609.P179 245 (1,5,7L,7M,35L,35M) L.M L (49M) 491.12251.20632921.P57 M (49L) 648128907712931.11193638545408118035815864041.P29 246 (2,6,82) 996301.11597586727284889.P114 247 (1,13,19) 666901.1037401.P171 248 (8) 1489.1082033636452177.525734876467633171387358753.P158 249 (1,3,83) 499.516012927768747007.P119 250 (2,10,50) 5*.685001.8140001.611302001.3169323413304763812001. .79347390994238721045338817576709220262296539001.P79 251 (1) 2478471208462211.2504680205769399125418017. .7398843004360382226199778563176650882609.P132 252 (4,12,28,36,84) 894097.5807636353.497067486989473. .1242952312910322705348673.478817600550381337769298251569.P38 253 (1,11,23) 23*.69829.4603589.5380969463. C164 254 (2) 509.3049.15241.23128733.232858973932476553. C178 255 (1,3,5,15,17,51,85) 13791727021.77847328539923823402265321321.P70 256 2*.28667393.126575155274810369.P192 257 (1) 1065004403.1967820731.6524149573. C189 258 (2,6,86) 14449.4084141.384439093.P123 259 (1,37) L.M L (7L) 269879.70067387496614602431591410975206848853.P49 M (7M) 4022839801.2057255879241720282007.465664617566727851156624881.P34 260 (4,20,52) 521.1739517065396641961.244465891693615564961.P121 261 (1,3,9,29,87) 8353.10117999187011.15093933143414026146604003. .8155614065469213507617261089.P72 262 (2) 4765781.2168567189.17553405361133.22135549699993. .13560715273664385557.P158 263 (1) 1579.5261.90084871694329.22552683088834321065574849.P176 264 (8,24,88) P136 265 (1,5,53) 11131.33391.4022224611747491.142949834073468649387631. .26026387361789965384243989827429482587206409750248632489022411.P68 266 (2,14,38) 131715756748633.9896074953947257550569260433. .9103517672844405140765408864689. .53237225364480041068705634426779969455366569.P66 267 (1,3,89) 495134413.P141 268 (4) C224 269 (1) 284626165115969876013103.P203 270 (2,6,10,18,30,54,90) 68347801.154625887441.2295769290481. .149009724864611641.68567709277540022540929078685056741.P39 271 (1) 4337.275566351.24272271317137.18578258282539321529.P184 272 (16) 5441.125060755002083736173971814320289. C181 273 (1,3,13,39) L.M L (7M,21M,91L) 674857.1621621.P50 M (7L,21L,91M) 547.539795803.174958633832822113.P32 274 (2) 4933.13433296255033.171346228229597943670543645694319949. C178 275 (1,5,11,25,55) 3301.390042354509501.P151 276 (4,12,92) 530122269701621893033.5068394466355183450313378335551130897.P92 277 (1) 1663.81439.3045893.588286507.76443543191.305666773213. .35666484627504843161821.C165 278 (2) 2434989769.270980007941.10311220574264857306049.P191 279 (1,3,9,31,93) 1117.161263.2458549.2015984789029. .37181027273307023448030259.21997634133124705942517215606813138917763.P60 280 (8,40,56) 9691924412174719842472801.P138 281 (1) 6631039.22239047886922111388109709879782334859. C193 282 (2,6,94) 1129.86857.23146232881. .8507408135928822982973809812954510818773.P98 283 (1) 1069846697769288119.P221 284 (4) 23857.148249.1267394873.190442563479129737. C201 285 (1,3,5,15,19,57,95) 643475985978004141.188783917797883464042250083871.P75 286 (2,22,26) 148171453.863977699157.680772171302969384246346369013813.C150 287 (1,41) L.M L (7M) 175804721.8005403352699006217853.9434065448210481479155118150417.P40 M (7L) 1723.13903914179.1463273844607.266604208732109666783.P56 288 (32,96) 577.86533516346363137.P143 289 (1,17) 185539.265229252768157343110127.92511297531161087879268599. C176 290 (2,10,58) 1741.47137463621.156998159690501. .417686802890095486149791834048621.P129 291 (1,3,97) 4197967.4883462672030653.6350450713263866826214495081.P113 292 (4) 27160673.6181086196826924696146082929. .9873849114499026811699931887107121.P175 293 (1) 395065379.9090234837292954970767.227144291051573623617426972653.C187 294 (2,6,14,42,98) 15289.7846427233. .262237634391526303909275720052818034806073.P87 295 (1,5,59) 84961.14329331.94424191.751440502001723166551.P156 296 (8) 593.1777.15731809.274166594399233.396632319992796527936468929. C190 297 (1,3,9,11,27,33,99) 4159.14357519353.707165317783. .409803998010903979377841.P103 298 (2) 36290833944740436954817.P228 299 (1,13,23) 599.1410683.746472099748883.25291032111194818151. .7100637712713772555039933861459. .26646467325353629274152005432430189091.P112 300 (4,12,20,60,100) 601.100801.3189188880923487431401. .61852110266729382934188518364722401.P72 301 (1,43) L.M L (7M) 3011.5504069054303.P90 M (7L) 171571.P102 ------------------------------------------------------------------------------- 315 (1,3,5,9,15,45) L.M L (7M,21M,35L,63M,105L) 2521.16381.934291.P48 M (7L,21L,35M,63L,105M) 631.118974628711.P47 329 (1,47) L.M L (7L) 92779.P113 M (7M) 659.1714104805001.P102 343 (1,7L,7M,49L,49M) L.M L 2722731943.568927133840129.141067436349500417. .20313193382308673633557.P61 M 32442313.10724186844800812803083930897.P89 357 (1,3,17,51) L.M L (7M,21M,119L) 772585843.2202998449.P64 M (7L,21L,119M) 6756409737221257.1485662731036994178049477733239.P35 371 (1,53) L.M L (7L) 1820869.228185777. .1289606659429174996411620359079305852855705254274280257.P64 M (7M) 743.999266838007025198420629785638217716921. .443586732305828439157807569986953963560622061.P45 385 (1,5,11,55) L.M L (7L,35M,77M) 331871.P96 M (7M,35L,77L) 1466073841.1258096891591.P81 399 (1,3,19,57) L.M L (7L,21L,133L) 9868867.1670786475971563131721697851.P57 M (7M,21M,133M) 1597.429406297507783.64008944055992470821992391547.P45 413 (1,59) L.M L (7L) 827.31036077322741. .40991599138422796033459901850750268659422849367762081133062231001.P67 M (7M) 4957.83426014043.64442922154738163.262909913482545708331. .17528277301916173559051083.P70 427 (1,61) L.M L (7M) 3344317139297.145599641870136959.3646347128361088619014438417.P95 M (7L) 1709.835213.8052785365241.309439649561434666017980378843611.P99 441 (1,3,7L,7M,9,21L,21M,63L,63M) L.M L (49L,147L) 7057.2658349.394387183.18506674369. .210814490395058681119744912719151.P46 M (49M,147M) 28473607.14154038259733.115759514862686269. .1001914514798811391.11150854626101679939871.P29 455 (1,5,13,65) L.M L (7L,35M,91M) 39368202746181575651477996103158141.P87 M (7M,35L,91L) 21841.20416811364869616971.P99 469 (1,67) L.M L (7M) 3745249137936077575894219292545707110891285448085229305573219.P107 M (7L) 1877.58113289356699002427121. .40809029414603235276963227708687836291.P105 483 (1,3,23,69) L.M L (7M,21M,161L) 1933.51199.2152701447163.33127892504734987. .82816799850795351486361063.P50 M (7L,21L,161M) 967.612139711.316122430589196488923. .37728367948485501911947.129343883108037584587651.P34 497 (1,71) L.M L (7M) 727354553235428733469289.16140614228102499143832286457.P125 M (7L) 295219.9182573.242556962948881834246849409.P140 511 (1,73) L.M L (7M) 6133.9199.61678723. C167 M (7L) P184 525 (1,3,5,15,25,75) L.M L (7L,21L,35M,105M,175L) 17851.2982139333951.12866510764382766303751. .3258624224115672560243320051.P36 M (7M,21M,35L,105L,175M) 1051.519071701.82189065001.111649516421101. .265320057244106443142346301.P39 539 (1,7L,7M,11,77L,77M) L.M L (49M) 521096004795829.793835915139705265367. C142 M (49L) 440903.P172 553 (1,79) L.M L (7M) 3319.19336199.379794871.72021557595389137. C162 M (7L) 560276508936447227.66240373517962417335857.P158 567 (1,3,9,27,81) L.M L (7L,21L,63L,189L) 1150005277.7657984783.18893984137732812609271.P96 M (7M,21M,63M,189M) 74553553407147697.550365355317860186830834043508553.P88 581 (1,83) L.M L (7L) 1163.P206 M (7M) 10459.156909509.199728047.1859414971.P178 595 (1,5,17,85) L.M L (7L,35M,119M) 210631.3179225740586661416281.P135 M (7M,35L,119L) 9291484250876801.775341901787730204901. .12448594440581981295316991.31555413494012729293961731.P76 7^{7h}+1=(7^h+1)L.M, L=T^3-B, M=T^3+B, T=7^h+1, B=7^k(T^2-7^h), h=2k-1. Table 10- Factorizations of 10^n-1, n odd, n<330 n Prime Factors 1 3.3 3 (1) 3*.37 5 (1) 41.271 7 (1) 239.4649 9 (1,3) 3*.333667 11 (1) 21649.513239 13 (1) 53.79.265371653 15 (1,3,5) 31.2906161 17 (1) 2071723.5363222357 19 (1) 1111111111111111111 21 (1,3,7) 43.1933.10838689 23 (1) 11111111111111111111111 25 (1,5) 21401.25601.182521213001 27 (1,3,9) 3*.757.440334654777631 29 (1) 3191.16763.43037.62003.77843839397 31 (1) 2791.6943319.57336415063790604359 33 (1,3,11) 67.1344628210313298373 35 (1,5,7) 71.123551.102598800232111471 37 (1) 2028119.247629013.2212394296770203368013 39 (1,3,13) 900900900900990990990991 41 (1) 83.1231.538987.201763709900322803748657942361 43 (1) 173.1527791.1963506722254397.2140992015395526641 45 (1,3,5,9,15) 238681.4185502830133110721 47 (1) 35121409.316362908763458525001406154038726382279 49 (1,7) 505885997.1976730144598190963568023014679333 51 (1,3,17) 613.210631.52986961.13168164561429877 53 (1) 107.1659431.1325815267337711173.47198858799491425660200071 55 (1,5,11) 1321.62921.83251631.1300635692678058358830121 57 (1,3,19) 21319.10749631.3931123022305129377976519 59 (1) 2559647034361.4340876285657460212144534289928559826755746751 61 (1) 733.4637.329401.974293.1360682471.106007173861643.7061709990156159479 63 (1,3,7,9,21) 10837.23311.45613.45121231.1921436048294281 65 (1,5,13) 162503518711.5538396997364024056286510640780600481 67 (1) 493121.79863595778924342083.28213380943176667001263153660999177245677 69 (1,3,23) 277.203864078068831.1595352086329224644348978893 71 (1) 241573142393627673576957439049.P41 73 (1) 12171337159.1855193842151350117.P44 75 (1,3,5,15,25) 151.4201.P35 77 (1,7,11) 5237.42043.29920507.P45 79 (1) 317.6163.10271.307627.49172195536083790769.P43 81 (1,3,9,27) 3*.163.9397.2462401.676421558270641.P27 83 (1) 3367147378267.9512538508624154373682136329.P42 85 (1,5,17) 262533041.8119594779271.P43 87 (1,3,29) 4003.72559.P48 89 (1) 497867.103733951.104984505733.5078554966026315671444089.P39 91 (1,7,13) 547.14197.17837.4262077.43442141653.316877365766624209.P27 93 (1,3,31) P60 95 (1,5,19) 191.59281.63841.1289981231950849543985493631.P33 97 (1) 12004721.846035731396919233767211537899097169.P54 99 (1,3,9,11,33) 199.397.34849.P51 101 (1) 4531530181816613234555190841.129063282232848961951985354966759.P41 103 (1) 1031.7034077.P93 105 (1,3,5,7,15,21,35) 30703738801.625437743071.P26 107 (1) 643.999809.9885089.215257037.2386760191.511399538427507881. .646826950155548399.P38 109 (1) 1192679.712767480971213008079.5295275348767234696493.P60 111 (1,3,37) 37*.30557051518647307.8845981170865629119271997.P29 113 (1) 227.908191467191.P98 115 (1,5,23) 31511.19707665921.20414137203567631. .5799951513941382144830754391.P30 117 (1,3,9,13,39) 240396841140769.537947698126879.3352825314499987.P28 119 (1,7,17) 923441.3924966376871.768736559421401249042753476963.P48 121 (1,11) 15973.38237.274187.P96 123 (1,3,41) 1811791.626920594693.9425856976319889649.P43 125 (1,5,25) 751.1797655751.176144543406001.P74 127 (1) 18797.90679.P117 129 (1,3,43) 210769832431.407429732767505248479163.P50 131 (1) 80173.109517.141811693.446790173.7370364319027.15594845538029429933. .7317723970031057677693.131758351065116151205213.P27 133 (1,7,19) 1597.2021015460335957.P90 135 (1,3,5,9,15,27,45) 1577071.16357951.310362841.258360989311.P39 137 (1) 2467.2535528323.1029879756928762117455431. .140175894162990609843314797.P74 139 (1) 119124859925363.P124 141 (1,3,47) 283.721030498171501831.P72 143 (1,11,13) 2823679.180523201.47428676444591705727929369346443.P74 145 (1,5,29) 9605671.15589280974996818911. .80684370001269698853996151670133742711.P48 147 (1,3,7,21,49) 63799.4715467.267652966241599.2603941883787374089.P40 149 (1) 12517.535596779200919.P130 151 (1) 907.429360649.29877981480806017715604631. .28656552837574546515657117360191971140211910788651135283.P58 153 (1,3,9,17,51) 307.18973.11910133.25332185271529.41331541464123787.P53 155 (1,5,31) 311.9294566806081.P105 157 (1) 301670477.5180282664612031.11427999892821876397004936937893.P101 159 (1,3,53) 351391.3852774594841.185328247384490197483.P66 161 (1,7,23) 6763.472341157.11273170771131750391. .1626777403161656797092007877.P74 163 (1) 5764066668537270911379761. .403925722833778378107304989280994102850314855068615959021587563.P75 165 (1,3,5,11,15,33,55) 471241.138267770127916457629034873443951.P43 167 (1) 18843947.106811083848465643. .37576897811119167463436962410483708090653.P102 169 (1,13) 11831.2709246550432452192307438140153898730002165574677.P104 171 (1,3,9,19,57) 229162071140015324614111. .1104249349362995181144668003642191.P52 173 (1) 347.21528169344472027. .46194618816084982100679234312974236345786346173.P107 175 (1,5,7,25,35) 18525843918490695886751.991474271662986957800680951.P71 177 (1,3,59) 3187.232199557797964905143390121842739619033812919.P69 179 (1) 359.36558961.4201521652717.352543640588653.P141 181 (1) 12671.28865519.995130761.16814655289.414479952329.P138 183 (1,3,61) 2520277. .26384856922809741239246281240888980994567902544116187.P62 185 (1,5,37) 6511230041186560022095681.1936570114827069923550119591. .63441573295906607253783211246544893041361.P52 187 (1,11,17) 143899867.19886424182370875870239184131623563.P118 189 (1,3,7,9,21,27,63) 878075126908698927928483. .33030636037992147205820927521.P56 191 (1) 4473297929.112103021940812743353521.P158 193 (1) 773.39373.561470969.639701219449517.4274417556076113498947. .26409540111952717487908689681403. .447798287131284928051408304965265782892174953181087929.P55 195 (1,3,5,13,15,39,65) 1951.35081393881.360924572424391.P68 197 (1) 52009.79040479805615687465683. .3599474961483053310878605135585111374469138078226023233589649293.P105 199 (1) 797.29453.2253079.P185 201 (1,3,67) 1609.2046166739518832881. .184976479633092931103313037835504355363361.P70 203 (1,7,29) 18620680471.68616805173400502243.223072327648229020879.P118 205 (1,5,41) 41*.275521.21158848681.P143 207 (1,3,9,23,69) 109908191603107. .823799348530495507269035013254489287846904557.P74 209 (1,11,19) 257489.1246477.9269802917. .42545662673095831743789692955596677.P124 211 (1) 692624557324389620662782322677336711138108482588281739734\ 375570506492391931849524636731866879.P118 213 (1,3,71) 853.1594093.1182534679.17469229933.P112 215 (1,5,43) 431. .41398275939670867448911914339156680381343777006826487831.P110 217 (1,7,31) 3662093. .51508652116008872412773338336289708669037765081397085489.P118 219 (1,3,73) 439.2212293763. .39316310783659104892252157287077969239619734325044334592964583271.P68 221 (1,13,17) 443.1661422610776235605151630089.P163 223 (1) 2677.130975483. C211 225 (1,3,5,9,15,25,45,75) 2002877551.2636899200194401. .97671987485517534751.125899659866627764313267482289910001.P41 227 (1) 113136621886721. C212 229 (1) 9161.43544351.9006996017757809392117.P195 231 (1,3,7,11,21,33,77) 2311.22187551.535212994471849. .234904066377148960506871003.156813120797253579231191970121.P40 233 (1) 467.47533.115081654907.89412401116867.42983757528467293. .10857980200444401822643.C162 235 (1,5,47) 518203357921.190893195970004711.1589908647339072250321. .605431706028029946531059199512572282414786250085768871.P80 237 (1,3,79) 90758677.1603873536486496162414778277997333003.P112 239 (1) 479.142847911. C228 241 (1) 125997820213. C229 243 (1,3,9,27,81) 3*.411361786890737698932559.P138 245 (1,5,7,35,49) 336737801.23609565631.8274923251622825388807721. .74689140199104459031993110210054016743223513365511.P75 247 (1,13,19) 1483.1024516164479902988921.1299823520026173021751. C171 249 (1,3,83) 4483.1413141919363039. .79631228080621938573499710253940180960724841. .3524445389714777887659796421466286321350017806951.P53 251 (1) 52371653.P243 253 (1,11,23) 1013.3037.72932311.2615313691182114927177553117.P179 255 (1,3,5,15,17,51,85) 77967508765681.17452955481423492661946457391. .34194473116159546979818689031.P58 257 (1) 1017721.4271961427. C241 259 (1,7,37) 2591.64638631.3663802449983927390483. .68941184253610253169908132923.P155 261 (1,3,9,29,87) 523.670249.44974999.9113995243.7299238406959. .9136734149894295938064503769037. .131108694538423601496731528051392288744803439.P54 263 (1) C263 265 (1,5,53) 116721153193946736160194298023751.P176 267 (1,3,89) 9613.540913940517169.P158 269 (1) 5418307589425009.44052813154697065841. C233 271 (1) 1627.56369. C263 273 (1,3,7,13,21,39,91) 1093.32786209.139708570703521. .5331924088485663758835996822909123141656859869805374791.P65 275 (1,5,11,25,55) 7151.15401.59951.2495283264895779020253203931608951.P154 277 (1) 1016157022810759.102092644289739525085919338335107091799. C224 279 (1,3,9,31,93) 18989357081041. C167 281 (1) 563.2597610354323.380431988961690791. C248 283 (1) 16809360945688609. C266 285 (1,3,5,15,19,57,95) 18449288550044654139241919401. .844267447094321323435601792968017601. .219414044208440803345204019137889332111.P42 287 (1,7,41) 1723.13365428707.1941851180301719. C212 289 (1,17) 42773.93195753455238027770502373.P242 291 (1,3,97) 1747.18043.1625625533641.1953725183587.1012047221926483.P145 293 (1) 587.9476124263231731100867. C268 295 (1,5,59) 366111286951.215168431547401.6898649252938113791.P188 297 (1,3,9,11,27,33,99) 55243.198397.1981560241.31600574312077. .165426670443186506567467. .7907009307594694001053552000588658391100974093457603716419437.P64 299 (1,13,23) 599.646777215499244129.P244 301 (1,7,43) 821856609631.13403893556831. C227 303 (1,3,101) 2096761.272295362253883.P180 305 (1,5,61) 1831.2441.38981441.23886931441.2589575105599981821056130911. .119724826129796860249638217747306760831.C150 307 (1) 526199.100066684713521521.11357792009472146190882003383320587841.P247 309 (1,3,103) 167798066344417387.3462948230491376473027. C166 311 (1) C311 313 (1) 1879.2099818661161079.P294 315 (1,3,5,7,9,15,21,35,45,63,105) 631.142809770881.P131 317 (1) P317 319 (1,11,29) 723493.798763879.25815444138362212501215782602427193330961.P225 321 (1,3,107) 167805961.P204 323 (1,17,19) 851908127328669427. C271 325 (1,5,13,25,65) 77351.200201.4347195468174001.280672874149406424401.C194 327 (1,3,109) 1147117.13675561831.46553630477420371690681.P178 329 (1,7,47) 1964089881669809395643. C255 Table 10+ Factorizations of 10^n+1, n<=330 L,M for n=20k-10<=650 n Prime Factors 1 11 2 101 3 (1) 7.13 4 73.137 5 (1) 9091 6 (2) 9901 7 (1) 909091 8 17.5882353 9 (1,3) 19.52579 10 (2) L.M L 3541 M 27961 11 (1) 11*.23.4093.8779 12 (4) 99990001 13 (1) 859.1058313049 14 (2) 29.281.121499449 15 (1,3,5) 211.241.2161 16 353.449.641.1409.69857 17 (1) 103.4013.21993833369 18 (2,6) 999999000001 19 (1) 909090909090909091 20 (4) 1676321.5964848081 21 (1,3,7) 7*.127.2689.459691 22 (2) 89.1052788969.1056689261 23 (1) 47.139.2531.549797184491917 24 (8) 9999999900000001 25 (1,5) 251.5051.78875943472201 26 (2) 521.1900381976777332243781 27 (1,3,9) 70541929.14175966169 28 (4) 7841.127522001020150503761 29 (1) 59.154083204930662557781201849 30 (2,6) L.M L (10L) 61.4188901 M (10M) 39526741 31 (1) 909090909090909090909090909091 32 19841.976193.6187457.834427406578561 33 (1,3,11) 599144041.183411838171 34 (2) 28559389.1491383821.2324557465671829 35 (1,5,7) 4147571.265212793249617641 36 (4,12) 3169.98641.3199044596370769 37 (1) 7253.422650073734453.296557347313446299 38 (2) 722817036322379041.1369778187490592461 39 (1,3,13) 13*.157.6397.216451.388847808493 40 (8) 5070721.19721061166646717498359681 41 (1) 2670502781396266997.3404193829806058997303 42 (2,6,14) 226549.4458192223320340849 43 (1) 57009401.2182600451.7306116556571817748755241 44 (4) 617.16205834846012967584927082656402106953 45 (1,3,5,9,15) 29611.3762091.8985695684401 46 (2) 1289.18371524594609.4181003300071669867932658901 47 (1) 6299.4855067598095567.297262705009139006771611927 48 (16) 97.206209.66554101249.75118313082913 49 (1,7) 197.5076141624365532994918781726395939035533 50 (2,10L,10M) L.M L 7019801.14103673319201 M 60101.1680588011350901 51 (1,3,17) 291078844423.377526955309799110357 52 (4) 1580801.632527440202150745090622412245443923049201 53 (1) 9090909090909090909090909090909090909090909090909091 54 (2,6,18) 109.153469.59779577156334533866654838281 55 (1,5,11) 331.5171.20163494891.318727841165674579776721 56 (8) 113.73765755896403138401.119968369144846370226083377 57 (1,3,19) 1458973.753201806271328462547977919407 58 (2) 349.38861.618049.11811806375201836408679635736258669583187541 59 (1) 1889.1090805842068098677837.4411922770996074109644535362851087 60 (4,12,20) 100009999999899989999000000010001 61 (1) 81131.11205222530116836855321528257890437575145023592596037161 62 (2) 2049349.483128549554512237305554588359039822397307149685578249 63 (1,3,7,9,21) 5274739.189772422673235585874485732659 64 1265011073.15343168188889137818369.515217525265213267447869906815873 65 (1,5,13) 131.8396862596258693901610602298557167100076327481 66 (2,6,22) 5419170769.789390798020221.2361000305507449 67 (1) 909090909090909090909090909090909090909090909090909090909090909091 68 (4) 152533657.65552746171882583264230070868884366877803237222654400793 69 (1,3,23) 31051.143574021480139.24649445347649059192745899 70 (2,14) L.M L (10M) 421.848654483879497562821 M (10L) 3471301.13489841.60368344121 71 (1) 290249.P65 72 (8,24) 8929.P45 73 (1) 293.10826684964539959837294043117.P42 74 (2) 149.3109.111149.708840373781.669031686661427842829.P29 75 (1,3,5,15,25) P41 76 (4) 457.1403417.5240808656722481737.P45 77 (1,7,11) 463.24179.590437.7444361.4539402627853030477.P22 78 (2,6,26) 3121.53397071018461.P31 79 (1) 1423.9615060929.P65 80 (16) 1634881.18453761.947147262401.P39 81 (1,3,9,27) 1459.2458921051.456502382570032651.610600386089858349939139 82 (2) 68389.P76 83 (1) 167.997.3565183.2097307081.7742098247001476863.P42 84 (4,12,28) 11189053009.603812429055411913.148029423400750506553 85 (1,5,17) 87211.787223761.P51 86 (2) 338669.P79 87 (1,3,29) 638453709757.135080726389891.P31 88 (8) 10100113.P73 89 (1) 179.12147237304901893.P70 90 (2,6,18) L.M L (10L,30L) 1105097795002994798105101 M (10M,30M) 181.4999437541453012143121 91 (1,7,13) 21705503.P65 92 (4) 2393.P85 93 (1,3,31) 373.44641.3590254957.P44 94 (2) 45121.2144906157509411684424913774078958939881.P49 95 (1,5,19) 1812604116731.121450506296081.P46 96 (32) 193.769.1253224535459902849.P41 97 (1) 102527361354613106010527.323338434891034089173475790125293.P41 98 (2,14) P84 99 (1,3,9,11,33) 7093127053.P51 100 (4,20) 401.1201.1601.P72 101 (1) 607.809.1213.1327067281.P83 102 (2,6,34) 409.3061.5969449.134703241.225974065503889.P29 103 (1) 1237.44092859.102860539.984385009.612053256358933. .182725114866521155647161.P37 104 (8) 1249.49297.300977.648961.249227787818677482257.P57 105 (1,3,5,7,15,21,35) 29970369241.1661378260814161.18276168846821336356291 106 (2) 1061.5051749.245391150214875249502685807421982149521.P56 107 (1) 1499.28463.74687.392263.795653.P82 108 (4,12,36) 1726290008991504500177463302688697.P39 109 (1) 3338786746233023.14060959683864286267405933000927102019.P56 110 (2,22) L.M L (10M) 661.148721.P32 M (10L) 18041.1121407321.P28 111 (1,3,37) 223.4663.21606064498691505246200058094681.P35 112 (16) 673.43735845217.217860610452031121598489279950204653537.P45 113 (1) 4973.4426889.P102 114 (2,6,38) 229.2281.4789.304077901.52875286008709.739653893349540289.P23 115 (1,5,23) 691.P86 116 (4) 233.355193.21591416633.17468739848498438039329935679794457.P60 117 (1,3,9,13,39) 461917.60034573.P59 118 (2) 430148941.P108 119 (1,7,17) 1868879293.5673320472670315859129.P66 120 (8,24,40) 1132716961.281259985248437790051014401.P29 121 (1,11) 11*.4357.25169.1485397.102502981431359171598893.P72 122 (2) 1587221.81183810541.101444162656037151745878558385892753596849.P62 123 (1,3,41) 739.148339.16419517.P65 124 (4) 1489.640543322297.27908132670449.384705444182230291105649.P68 125 (1,5,25) 21001.162251.10893295001.P81 126 (2,6,14,18,42) 1009.43266855241.P59 127 (1) 3557.857772733.1094479651.1125629957.616896149073719728613. .10860110813777339731289.P53 128 257.15361.453377.P116 129 (1,3,43) 304768036847074491064894608014695867632997.P43 130 (2,26) L.M L (10L) 1031498834064949381.P31 M (10M) 2311921.12763852652999774041.12119730504567977254081 131 (1) 263.1397382241.306662501757259.525786373041914526306757. .112506283680098168752627601991569.P49 132 (4,12,44) 2377.16369.432961.6796152793.24387741577. .126197002179733470481.P27 133 (1,7,19) 247025236977306025681323889. .61828645758322140842666144519962696417487.P41 134 (2) 269.4021.260587121.94927228208573594069. .2302527353565357450759725122262880394277261.P56 135 (1,3,5,9,15,27,45) 6481.577603663291.31023833790241.P43 136 (8) 17*.13355595217.P117 137 (1) 364393423.117651465889.441651480271681.676321006412903. .218801242136856556680173235529.P58 138 (2,6,46) 829.1569889.536430531035337769.757108543129939106221.P41 139 (1) 557.2503.P132 140 (4,20,28) 851761.P91 141 (1,3,47) 344887.9127213.1160803383934463712259.P59 142 (2) 569.7669.380623849488714809.7716926518833508778689508504941. .93611382287513950329431625811490669.P50 143 (1,11,13) 51767.22144088539.264752347289.104730101107272149081.P74 144 (16,48) 13249.1067329.P86 145 (1,5,29) 1451.30104611.58765601.2433146345771.17996132431060961.P65 146 (2) 5911541.16692085818029.5774294197526381. .182202742802607835615596881.P82 147 (1,3,7,21,49) 7*.P84 148 (4) 61544617.16444765848115921.P120 149 (1) 2087.9615683031450065714899. .165459609176797865866134365329792270635207840943.P76 150 (2,6,10L,10M,30L,30M) L.M L (50L) 261301.P35 M (50M) 601.3903901.168290119201.25074091038628125301 151 (1) 181288487.153653579173.12331942624071394811. .2646756758131654397378192081701748003041997.P69 152 (8) 134369.31735795756961.P126 153 (1,3,9,17,51) 2142001.5364487.832339891.276402747619.2405782797823.P51 154 (2,14,22) 39511854229.P110 155 (1,5,31) 11161.3925963357681.5167617497664851.P88 156 (4,12,52) 313.1101673.1358074433371719716641.291593563046646669491593.P43 157 (1) 4397.3641773.P146 158 (2) 5689.507998564486483655774880939989709. .646301962916453492325383567253991760083617720844121.P69 159 (1,3,53) 3499.2784091.54137839415767.917813298871770308465539. .26526333976234009593263527.P31 160 (32) P128 161 (1,7,23) 967.1569936761.1203881882727712699967. .23391028206417273637358380573.7775058388319250595762800404689.P40 162 (2,6,18,54) 2925721.P102 163 (1) 653.13693.14286890032106357. .66953479943839030979655991920753816099754871899.P93 164 (4) 121553521.36637591407529194237097.P130 165 (1,3,5,11,15,33,55) 4124507971.19835636682880495867311241.P46 166 (2) 23023967955265160767768376873521136169786061.P121 167 (1) 63716179.116011189311149998139.272828068791212993437. .301525294918950432087520298129941558711551656822567015411.P62 168 (8,24,56) 337.2070270028985341766616009080161.P64 169 (1,13) 677.987001237. .1592730232155679902273246343099578009020762979379345291.P90 170 (2,34) L.M L (10M) 7568346838961.237612993541791006121.P31 M (10L) 26861.P61 171 (1,3,9,19,57) 19*.2053.4410785971.2911579215499. .307010852070382484317401373.P55 172 (4) 277641151780258438310079109077611969. .2645778409917434965592366282025495569. .38993135849791157061060738352944105076217.P56 173 (1) 9689.16864733.P161 174 (2,6,58) 997369.15565833747318241.157002934023127338801841. .4477350074169470752905544969081.P36 175 (1,5,7,25,35) 3612546001.299547376801.P99 176 (16) 11969.4913921.470909313601.P138 177 (1,3,59) 60247408327.968385024074451409.2676157881043509853. .3203031926532314264104769060847481.P36 178 (2) 38449.138841.P167 179 (1) 523661705392754764972834211810001059.P143 180 (4,12,20,36,60) 265183201.95853807664312827399794371014650641.P53 181 (1) 13757.1467439874822650361.5781376922797866530410940379929\ 1636496876923883191635824278127299864929561.P84 182 (2,14,26) 654721485601. .3571618567996393297210217238290456648947344377957590363519828421.P69 183 (1,3,61) 367.51745081.40498340376691. .42936744040512685057308971520417028077990465463.P50 184 (8) 120553054891405588545727822543281066162803459003848166118314367809.P111 185 (1,5,37) 49173925574833481.P128 186 (2,6,62) 5209.139716865184144864008269344660199946429.P79 187 (1,11,17) 192611.1284680342573.6315203673292075607. .125797399492676917721.P104 188 (4) 70313.79337.485041.118710721.6578404633. .169905327561162104198557246291921.P119 189 (1,3,7,9,21,27,63) 379.8642670625016390971. .63060936944326674212591995662102125143.P49 190 (2,38) L.M L (10M) 780548018657747948342675331841.P42 M (10L) 761.1901.3041.74861.417332341.P50 191 (1) 383.679961.4041943.955059211.78087485383. .3370796736173938091727422330529475982098304687381174810841794\ 785884893349397.P80 192 (64) 3457.12289.418725889.338579887181973006729167651681190977281.P74 193 (1) 1931.10037.1430131.166376423.P171 194 (2) 389.78412655334235167606162810513004420610966509546603404\ 268745999503561001.P119 195 (1,3,5,13,15,39,65) 15601.925081.P86 196 (4,28) 52781463673. .5010620991340707523594168804430658367520003649793780623118456073.P94 197 (1) 15761.7187743.300567477887394052365757. .29811355463297742645615812791522446524687.P121 198 (2,6,18,22,66) 79082656489.1538607523068637497164701.P85 199 (1) 3545105703277.10765760180213.12277415800813. .180724074168604579796294647309331. .314293140427626491056008875724151058487007.P86 200 (8,40) 24592788001.3475700719926956233659563848134955052440801.P108 201 (1,3,67) 7237.17830074841.851109498533797. .45360300267343173645804799921.P75 202 (2) 101*.3679329001.19384130081.12793360409007449. .4908990488743183603681.5383539446793990416488818114381662511041. .147987024898557331825270928295100820916509.P60 203 (1,7,29) 19489.243720583.2563963356465898129. .13569612563320403017443683179.P109 204 (4,12,68) 2857.13266937.1119527384827710553. .53043011765949537815976769.P74 205 (1,5,41) 436026711667335044426416921.P134 206 (2) 801341.29286597879221.33670587927455442579575167786879669. .95000575486937988681435170477136054984821.P110 207 (1,3,9,23,69) 37916801893.143409436964525899. .831759677425747570837717.117680633072620952134930832292859.P49 208 (16) 19725473.40336502753.754651871841089.49190086416352961.P143 209 (1,11,19) 419.85691.258743.P168 210 (2,6,14,42) L.M L (10M,30M,70L) 42681134161.424451728681.P27 M (10L,30L,70M) 1384194841.P39 211 (1) 2764617069785703725933625413.P183 212 (4) 18233.67406298457.1488067111584049.899319337247551841. .23641392997940421257. .54469179239047116300845682623717697162577784999950014081337618457.P76 213 (1,3,71) 2107849.21977699107816352490639478201.P106 214 (2) 40882343106721.P199 215 (1,5,43) 1721.18920435284033918144809657490533251.P131 216 (8,24,72) 433.491413179769291800875985377355914924161. .42329002505294251119371713750694841859239120433.P57 217 (1,7,31) 240437.1142669053.313360308665807383.579210707460230341693.P128 218 (2) 20929.143881.49369369412784246809.35701893527078181712481.P165 219 (1,3,73) 877.3601237.247482272761.5830219322612939561246246317093. .3943828696311504418317587369596960932033847171.P47 220 (4,20,44) 881.P158 221 (1,13,17) 344954191876997.6917979239326637.70919383630417672662131. .2016492306990976282439501774196098215666169.P97 222 (2,6,74) 23653713304547869.543309565743971477870075858731741. .2228457285782705288389843210675909.P62 223 (1) 208729.1697477.5156432569. C201 224 (32) 417067672004431016027567793820801. .707285850117624346067550937755073.P127 225 (1,3,5,9,15,25,45,75) 270001.P115 226 (2) 52743988481.132305743681936841. C197 227 (1) 36346333.3861904074787001.P203 228 (4,12,76) 27817.376102873.36120612721. .13591271120229398317886003161009.P90 229 (1) 2317091604522004723965449. .22122368173743271094350225612207534262957.C164 230 (2,46) L.M L (10M) 4107757827661.P75 M (10L) 461.509681.93744372901.8225357978845859081. .439120676164610394481.P30 231 (1,3,7,11,21,33,77) 8317.136094982876222218559943.P93 232 (8) 929.23201.182353.4465073. C205 233 (1) 552677.131293689927974865167. C207 234 (2,6,18,26,78) 11761957262582764997761. .117609798518967483441609863271124249.P87 235 (1,5,47) 5641.20681.21997411.P169 236 (4) 395026241.6218964172073.3410758635375200561. C193 237 (1,3,79) 6637.132247.P148 238 (2,14,34) 2381.275855329893529.20087794479102305428621. C152 239 (1) 508399838327574001. C221 240 (16,48,80) 177601.1786971871341978412769793172635403245447905376001.P75 241 (1) 11087.140263.166118970220264489. C214 242 (2,22) 56629.170369.29606281.1491164086760128255001869. C179 243 (1,3,9,27,81) 487.487.69499.67430557.P144 244 (4) 2438537.10399345405377216553. C215 245 (1,5,7,35,49) 491.18131.653518704357372488880162997801.P132 246 (2,6,82) 216667590115007379484962361. .83991579034720609392656974112397395006880745482841386049.P78 247 (1,13,19) 38816051.82266809. C201 248 (8) 789592121167489.866353530992835497979626513. C199 249 (1,3,83) 499.1442209.2184727. .8640537866821528796307988728455578923633637199851.P100 250 (2,10L,10M,50L,50M) L.M L 4001.76001.P92 M 1610501.P94 251 (1) 503.5213439677.4067568702062638144916699. .17764334637927138067713031681.2212012955306294098346533984373.P155 252 (4,12,28,36,84) 41593295521.7064204436768358634702473. .84127549110077880819608858067897680511169.P68 253 (1,11,23) 23*.6866927.134411715692212607377411.P189 254 (2) 509.3049.7621.47363086944961.621385610460229.P214 255 (1,3,5,15,17,51,85) 102001.5516286288241. .4270914986978327797975291.216219010761333454086082249502131.P54 256 10753.8253953.9524994049.73171503617.P225 257 (1) 30841. C252 258 (2,6,86) 8045181580990560114237163201. C141 259 (1,7,37) C217 260 (4,20,52) 120920505705101252491925533049923433521. C154 261 (1,3,9,29,87) 155557.2762580729671077856014459. .6811645794372004956047418049529911921.P102 262 (2) 1049.14149.33887081.45401981.322185369274849.P224 263 (1) 935875736987641.P247 264 (8,24,88) 75675153541982860202858401.11786300284844910479546815969.P107 265 (1,5,53) 538481.2040723131.3961565781890816563346704051.P166 266 (2,14,38) 2129.14691812549.1728095716605342484009. C182 267 (1,3,89) 3154339.118941438655807. C156 268 (4) 27316505681.179093946929. C243 269 (1) 269539.2582401.P257 270 (2,6,18,54) L.M L (10L,30L,90L) 329941.49229101.68189581.P51 M (10M,30M,90M) 541.13029637224192121671301.P48 271 (1) 3253.13631530938380353975492092299. C239 272 (16) 58627969. C249 273 (1,3,7,13,21,39,91) 102103.P139 274 (2) 718606649.40160350429. C253 275 (1,5,11,25,55) 1501539197401. C188 276 (4,12,92) 1657.1469409649.38115215074391056784287931569.P136 277 (1) 9419.9973.2583222779. C259 278 (2) 1669.154220035640400941. C256 279 (1,3,9,31,93) 1117.183372282864547916749018225828651.P145 280 (8,40,56) 1378721.5758943337281.6717658458758041138199521. .1081862991605594332069477594870669601. .70488250368897247920709885766793062547616862669921.P63 281 (1) 6560496291091.58513940129535379432477007. C242 282 (2,6,94) 1129.3792128943527581.2246285860430986548506215527001. C136 283 (1) 1699.241117.61945573305222690279363663578823967. C239 284 (4) 4672937.11473030297.273919647900781361. C246 285 (1,3,5,15,19,57,95) 571.11382273828031938028891. .43135513763991692454656851.P94 286 (2,22,26) 17576772101461.754309323029578981494450523147961. .4832227158939716614468345433242909.C161 287 (1,7,41) 19214818177409.P227 288 (32,96) 577.317752351489.P178 289 (1,17) 511438099.587063793048979091.42323992639419349049079264521. C217 290 (2,58) L.M L (10M) 1767955366388381478541.P91 M (10L) 14087942679857610940613213182901.P82 291 (1,3,97) C193 292 (4) 73*.1753.468953.162393769017609303761. C258 293 (1) P292 294 (2,6,14,42,98) C169 295 (1,5,59) 2353867026803341982771.25602601418102182972721. .193428272579096534429098931.803454205095303821868753731.P136 296 (8) 593.P286 297 (1,3,9,11,27,33,99) 7129.8927244623941181398233253. .1866763546567680996103417376059. .112970308382439859401726947341740704554951737408511354573.P65 298 (2) 10729.607921.136916416686052955621. C267 299 (1,13,23) 32494323733. C254 300 (4,12,20,60,100) 32401.4711806100010561082466291127577601. .4482637729513780747000872935673625025127940754401.P74 301 (1,7,43) 3613.212057054080446499.120525789336558438197. C212 302 (2) 15101.20481641. C289 303 (1,3,101) 133321.329059.389659. C184 304 (16) 3031489. C282 305 (1,5,61) 2447385101917578576518614756091. C210 306 (2,6,18,34,102) 54469.158963941.2709009355501.3626707988341. .157538980319816607121.846160494149365798478410729. .112544281755782732673671367061.P78 307 (1) 3311436805543.1490473286202873492575327109823. C264 308 (4,28,44) 53241089690155545084545617441. C212 309 (1,3,103) 619.P202 310 (2,62) L.M L (10L) P121 M (10M) P120 311 (1) 82727.2122689869717.7966595011106561.3416317897947415066069561. .835375365056917236891484436143.C223 312 (8,24,104) 148068337.10662171313.325807801400017. C160 313 (1) 5009.1074844665139845442819616837. C282 314 (2) 28415783195151364586816438858689. C281 315 (1,3,5,7,9,15,21,35,45,63,105) 2521.131041.525326613841. .1275784731048123659634702312820051.P91 316 (4) 259121.73921249.P299 317 (1) 3536453.12361733. C303 318 (2,6,106) 3181.125929.1650244260647104976802437090486126821.P164 319 (1,11,29) 1277.357281.49561573447. C261 320 (64) C256 321 (1,3,107) 7569823.2366998879807.899788378170104270110161037.P166 322 (2,14,46) 216613430183025989. C247 323 (1,17,19) 647.108529.738379.1644353478367.1078893279821424911891. C242 324 (4,12,36,108) 68562937. C209 325 (1,5,13,25,65) 107251.4271801.82009322851.318942474614140390001. C197 326 (2) 498698470009.76232914055207003005318654163381.P281 327 (1,3,109) P217 328 (8) 6051298241.48656086054529.669995415570582921859463287135169. C264 329 (1,7,47) 659.P274 330 (2,6,22,66) L.M L (10M,30M,110L) 507868012934701.6143203800519931376420641.P41 M (10L,30L,110M) 17247781.1082745841.18516980928601.9000931379651641.P35 ------------------------------------------------------------------------------- 350 (2,10L,10M,14,70L,70M) L.M L (50M) 701.422100001.1125310645201.P97 M (50L) 213567756617511209506778605497489645838025587933288349770601.P61 370 (2,74) L.M L (10L) 1481.6336499381. .271880675850180367872653023164942909880799363524216099671322919521.P67 M (10M) 15541.68821.74615611921.4098464044501.107771345624719321. .16206170837408945509907221.P69 390 (2,6,26,78) L.M L (10L,30L,130L) 201721695849323521.2685647186330706081032050321.P51 M (10M,30M,130M) 19501.9160020509281917601.P74 410 (2,82) L.M L (10L) 59090021.1266925593264677597290950641.P126 M (10M) 821.639601.11036695406441.1073380218518144441. .1350059351915828990550200161. .139074671904011778473984366758527524121792121.P49 430 (2,86) L.M L (10L) 7741.2198478623863901. .7549370642855106064318428883982856249713821.P107 M (10M) 1044817620601.P156 450 (2,6,10L,10M,18,30L,30M,90L,90M) L.M L (50L,150L) 1801.33301.139501.560701.5030101. .152372720018473862927761564984708391701.P57 M (50M,150M) P120 470 (2,94) L.M L (10M) 941.29096340761.474181059033108701.P153 M (10L) 18465110677523332168571918701. C157 490 (2,14,98) L.M L (10L,70M) 268330861.32422034720694602873554553373241.P129 M (10M,70L) 366395073564101.354434210886621881. .28706164502711390875680641913825481.P102 510 (2,6,34,102) L.M L (10M,30M,170L) 8161.2586721.5071197096181. .677827125083342723075551469213357648491441.P64 M (10L,30L,170M) 1021.855781. .114797635898427958794033542315180663747542680841.P72 530 (2,106) L.M L (10L) 10601. C205 M (10M) 4241.1103461. C198 550 (2,10L,10M,22,110L,110M) L.M L (50M) 2471701.486904001.133157371602664723858501. .212890462662706052906860201.49094895915282817628267672401. .3668996113223183559833250396711179251902642533701.P59 M (50L) C201 570 (2,6,38,114) L.M L (10M,30M,190L) 211592942161.481612717573381. .117008737749609201563737321.P93 M (10L,30L,190M) 20521.7594681.70532941.3685902392604541. .9025836525591423620461.14634428294824755331225520581.P59 590 (2,118) L.M L (10M) 193274561.347811486461.12013233555242641. .8505896978256278656680007081.P168 M (10L) 1181.35764621.3064985101. C213 610 (2,122) L.M L (10M) 21961.51241.9818561.28474644365651641.17716886277230798340041.C185 M (10L) 6101.217345835281.555818110301.8950221294967070861. .17751033585336286181.C176 630 (2,6,14,18,42,126) L.M L (10M,30M,70L,90M,210L) 158201922061.56541586842121464411050521. .229209947541611916250468549073491977346097487987121.P57 M (10L,30L,70M,90L,210M) 1351855459456741.33822732328831925621101. .19825744781339712457003608841.938366482703941691072746568832156530761.P40 650 (2,10L,10M,26,130L,130M) L.M L (50L) 1301.P237 M (50M) 431684501.23098714167966114959599501.P206 10^{10h}+1=(10^{2h}+1)L.M, L=A-B, M=A+B, h=2k-1, A=10^{4h}+5.10^{3h}+7.10^{2h}+5.10^h+1, B=10^k(10^{3h}+2.10^{2h}+2.10^h+1). Table 11- Factorizations of 11^n-1, n odd, n<240 n Prime Factors 1 2.5 3 (1) 7.19 5 (1) 5*.3221 7 (1) 43.45319 9 (1,3) 1772893 11 (1) 15797.1806113 13 (1) 1093.3158528101 15 (1,3,5) 195019441 17 (1) 50544702849929377 19 (1) 6115909044841454629 21 (1,3,7) 7*.1723.8527.27763 23 (1) 829.28878847.3740221981231 25 (1,5) 5*.3001.24151.1856458657451 27 (1,3,9) 5559917315850179173 29 (1) 523.303309617049998388989376043 31 (1) 50159.2428541.157571957584602258799 33 (1,3,11) 661.1453.637265428480297 35 (1,5,7) 211.42437717969530394595211 37 (1) 2591.36855109.136151713.2615418118891695851 39 (1,3,13) 79.157.547.84631.480091.32508061 41 (1) 83.1231.27061.509221.14092193.29866451.840139875599 43 (1) 1416258521793067.42534656091583268045915654719 45 (1,3,5,9,15) 9842332430037465033595921 47 (1) 2069.22666879066355177.18806327041824690595747113889 49 (1,7) 510810301.1065264019.100641220283951395639601683 51 (1,3,17) 10711.457315063.15085812853.25994736109 53 (1) 107.351497.6005113.6918082374901313855125397665325977135579 55 (1,5,11) 25301.39161.643170158708221.645654335737185721 57 (1,3,19) 19*.1047623475541.1412900479108654932024439 59 (1) 1181.70845409351.33083146850190391025301565142735000331370209599 61 (1) 440177.520518327319589.1461808298382111034194027645506019619578037 63 (1,3,7,9,21) 127.8317.867259.106431697.316825425410373433 65 (1,5,13) 131.673267426712748387612994804392183645147042355211 67 (1) 15277.2160349.76394148218203559.P42 69 (1,3,23) 139.8209475377.P34 71 (1) 1847.64327.159248456569.1273880539247.P42 73 (1) P76 75 (1,3,5,15,25) 151.59302051.1826934301.27665283091695977275201 77 (1,7,11) 593554036769.P51 79 (1) 317.185277551100523662054683911.P53 81 (1,3,9,27) 139026457.14010692617072784593.P29 83 (1) 167.12119.178057577.52447614013.P61 85 (1,5,17) 584916791.553393500180551.P44 87 (1,3,29) 398113.54415717.P45 89 (1) 73111721.2103114787086589.4180235017418376525776333.P44 91 (1,7,13) P75 93 (1,3,31) 2791.3163.P56 95 (1,5,19) 67989221.180124441029509240214675551.P41 97 (1) 389.4247091263.P88 99 (1,3,9,11,33) 397.2377.1240500097.P48 101 (1) 341459085477993311443.86408339296208914807632672776254957729.P46 103 (1) 24103.37723802531.995301206162659155091.P71 105 (1,3,5,7,15,21,35) 421.540751.599551.2598121.126713791.P22 107 (1) 1276033068038437.304971297664201988898688683700564748747693245597.P48 109 (1) 35970728459102446279558069.P87 111 (1,3,37) 651950416864148392635280596760630561.P40 113 (1) 227.45902861.20884152591287817709. .22455907106840364577416382241618449.P53 115 (1,5,23) 95911.333041.9964291.17184010031686356151.P55 117 (1,3,9,13,39) 9127.1810693.P65 119 (1,7,17) 239.20580793913.5787647502138040836760695667.P60 121 (1,11) 30977.1595696213.12407691244609.P88 123 (1,3,41) 174907.28385941.142971820992006871646588679396397417.P36 125 (1,5,25) 5*.1632185486501.27678437808551251.P75 127 (1) 2985212831443.6073732108394141.108345618426999904901.P83 129 (1,3,43) 1549.1389891409.2338110553.44012945778511. .3440126314390780951.P34 131 (1) 263.7791763956749016154215607697892626144401.P94 133 (1,7,19) 292601.1889399.4085166784889.P89 135 (1,3,5,9,15,27,45) 271.P73 137 (1) 8221.339761.3677081.136238281.394711476243912154244261783.P91 139 (1) P144 141 (1,3,47) 283.64192789.44682948968412414039336007.P60 143 (1,11,13) 3433.3111663528084541.191144869353686249. .39087214421959708068637.P67 145 (1,5,29) 38861.144801130358116982559692328954495371.P77 147 (1,3,7,21,49) 7*.6469.712319250521341.1965320765521339221407672989.P41 149 (1) 95648167.12386903337067381971073.P125 151 (1) 16944919.13665285883.18462023135737378116249335576687.P108 153 (1,3,9,17,51) 307.1531.35236819.25167354031.2926326645433. .290204982599509251565261308001.P35 155 (1,5,31) 112582632731.21008012759943211.12981042678412809421.P79 157 (1) 88388104773677.40715753678177846062481. .20186536221332782615476135581.5898938014844761247631748773851299.P64 159 (1,3,53) 1399201.2622229.23393486084531921650287976389757830429777373.P53 161 (1,7,23) 967.48359249.P127 163 (1) 391313358915050362321.1568405349185888385874441.P124 165 (1,3,5,11,15,33,55) 1321.121679581.1454598708730201.P57 167 (1) 2339.1353068069.312708742481.2371759568436871497727. .3523115712994289296116782558201078504837006181920850717652507.P67 169 (1,13) 2029.362685493. .5276574100195101793609935574565521674231026096229661942697690104397.P84 171 (1,3,9,19,57) 32491.406981.368030647.27361000362650239.P78 173 (1) 347.593979931.19313697101202731.P152 175 (1,5,7,25,35) 1849051.P119 177 (1,3,59) 31153.128857.77162089. .7005596150545816426029108678026870967790150254367.P55 179 (1) 359.260690365910973937.133424628147697995732126527. .30262061969946294833518392497.680728835990076713808763658029. .459009579117136530987907464707351.P49 181 (1) 42811641487.8439877927139263645774810523.P149 183 (1,3,61) 1640962831.470011312403953.252792952756496725399. .120213931658422906698644629.P55 185 (1,5,37) 3701.2341771441.8942042341.586894211641. .9469266456252868041356465741.111979611651060119297676530503786924451.P50 187 (1,11,17) 625293470077.1187896992833. .759915556656723468789897776052021738313604080983777078304038497.P80 189 (1,3,7,9,21,27,63) 757.2150969311.452555562844477. .5578141711502710729.36959230870280730074750882077.P39 191 (1) 195967. C193 193 (1) 1931.P197 195 (1,3,5,13,15,39,65) 50311.3762447001.P86 197 (1) 3012710549939.1060717191208815311.5407146368827614877351. .616346818465450400938401858863608277357.P114 199 (1) 797.140893.18242336369.4645373755026923. C173 201 (1,3,67) 1609.66046284412625914877623090150129. .14160915264340305525070590511634038738687.P63 203 (1,7,29) 5279.60901.490738600321966404709119573187611258997827\ 809661439583138969212062707.P98 205 (1,5,41) P167 207 (1,3,9,23,69) 2631980958036751.P123 209 (1,11,19) 6689.3107455009693.3215499310277.1056394526657537. .342732573655364605155483163584083618987113.P103 211 (1) 88672307809797915061.P199 213 (1,3,71) 4813252624072182882141229.44043095909867219792359537381.P93 215 (1,5,43) 431.133680121.6371112819065042612731.P143 217 (1,7,31) 29605139295060799. C171 219 (1,3,73) 439.4072194187. .514949924967851751873479083936952760941875001182553509.P84 221 (1,13,17) 27847.312937.3473237.1126168894058957269. .13720057759140780365187158337101.C135 223 (1) 453137.47060137.7672126756781.326495629795175719. .1368635346986648651098441242784461410529545236877.P140 225 (1,3,5,9,15,25,45,75) 5851.2438939252251.P109 227 (1) 14106056111465766059.1792798399719936463007. C195 229 (1) 84743741.15587642569099. C217 231 (1,3,7,11,21,33,77) 312313.6103043101.355797740761.662072596417. .10965056258773.P74 233 (1) 1399.2797.57401881.308184993449104253. .175138501604778346236805296173.C181 235 (1,5,47) 2351.14749541. C182 237 (1,3,79) 34273461979846373350261832761.P134 239 (1) 479. C246 Table 11+ Factorizations of 11^n+1, n<=240 L,M for n=22k-11<=473 n Prime Factors 1 2.2.3 2 2*.61 3 (1) 3*.37 4 2*.7321 5 (1) 13421 6 (2) 13.1117 7 (1) 1623931 8 2*.17.6304673 9 (1,3) 3*.590077 10 (2) 212601841 11 (1) L.M L 58367 M 23.89.199 12 (4) 10657.20113 13 (1) 53.911.59583967 14 (2) 29.1933.55527473 15 (1,3,5) 31.7537711 16 2*.51329.447600088289 17 (1) 71707.264793.2218331 18 (2,6) 3138426605161 19 (1) 191.229.83791.1390636259 20 (4) 41.1120648576818041 21 (1,3,7) 3421169496361 22 (2) 251857.2649263870814793 23 (1) 47.1013.241363.6493405343627 24 (8) 97.241.1777.1106131489 25 (1,5) 46601.14436295738510501 26 (2) 9768997162071483134919121 27 (1,3,9) 3*.379.4889988840047743 28 (4) 113.449.2521.77001139434480073 29 (1) 59.10979607179423.204064664440913 30 (2,6,10) 46329453543600481 31 (1) 311.1303.10789.3658524738455131951223 32 2*.193.257.21283620033217629539178799361 33 (1,3) L.M L (11M) 9439.991651 M (11L) 67.1169382127 34 (2) 137.2481791513.9598959833.641625222857 35 (1,5,7) 71.71.7561.17011.1649341.10047871 36 (4,12) 73.40177.3358335487319458201 37 (1) 2691614274040036601.10527743181888260981 38 (2) 1990415149.15403468930064931175264655869 39 (1,3,13) 313.63649.538953023961943033 40 (8) 5281.399806412551699044818733915681 41 (1) 711628063.1216150172449.479378523680060338823 42 (2,6,14) 19069.520799717831587692709 43 (1) 5333.9413099125139413690486707432096974989067 44 (4) 353.72689.13585441.1298256794387169996154165633 45 (1,3,5,9,15) 181.631.86306335830799838011 46 (2) 201757.2004414397.24737721275161.656943272596448809 47 (1) 844309.549524471.26097456317.60699948346804199382437 48 (16) 577.3659233404740477018363752843393 49 (1,7) 11467.800171.176784259.33761096386802842263303497 50 (2,10) 101.2248313994601.1993099906542710819727884501 51 (1,3,17) 103.1348033.16576413357576409067287639 52 (4) 97010607829826070873559937268360584022789501553441 53 (1) 1697.5353637.17148893.8357265774463208206521728596439861293 54 (2,6,18) 109.541.388174681.1350472353550875103121929 55 (1,5) L.M L (11L) 21537414911.85480219991 M (11M) 4951.411841.131525983711 56 (8) 337.394129.236352238647181441.3090443962383595123379137 57 (1,3,19) 6043.75013.74337838382167137728921322559 58 (2) 349.16585333.32637413.109181877624126996017801852385627698243261 59 (1) 22067.32833036072593109.59845177539010249.53199025841281128499153 60 (4,12,20) 52020741601.40589999671017742452961 61 (1) 53320740257.137218978667473446671.38147158686655703132426388314683 62 (2) 4311672901046383796549.70039146133823870629334170297294343364149 63 (1,3,7,9,21) 3304981.468843103.71596275661.278853374647 64 2*.316955440822738177.7032401262704707649518767703756385761576062060673 65 (1,5,13) 1301.25741.3160327139569513638485230516120919120957201 66 (2,6,22) 9863099401.46266666682081629547022793157801 67 (1) 269.181303.2354458793.2778466094669.76388592846687031.P23 68 (4) 409.11969.739755736441.14387579997041.P35 69 (1,3,23) 691.394648951.18013255921.932225927887.1577386579003 70 (2,10,14) 2970941.P44 71 (1) 149852362577.5604196051154865381517.P40 72 (8,24) 110161.331921.P40 73 (1) 668243.147031637.51866303408957.9863258277206753.P32 74 (2) 149.243595717.254246981.3275634569.5555901630889277.P31 75 (1,3,5,15,25) 751.299401.P34 76 (4) 457.35613601.52215193.P58 77 (1,7) L.M L (11L) 23577401.2040583524866430994330651 M (11M) 43037232701.160418704149053207551 78 (2,6,26) 13*.7177.26833.225889.21493057.11771471409361.683665316878909 79 (1) 7901.681676939.3238766178025207268898109882481893.P35 80 (16) 641.2081.4001.232961.295090738600481.1037593750081121.P23 81 (1,3,9,27) 3*.163.5705803.P47 82 (2) 2789.57073.P76 83 (1) 325440677.47433880332031195178437273.P52 84 (4,12,28) 201407641.70107576001.P31 85 (1,5,17) 34511.P63 86 (2) 173.11862832433.P76 87 (1,3,29) 13399.7596493.1727522113.P39 88 (8) 3169.269281.2224106369.1409524185566665684709841121.P38 89 (1) 179.188606309.5089163291.75893828851.23510589261592841. .371848407757843241773.353082502532286628861787 90 (2,6,10,18,30) 9001.16921.22501.P38 91 (1,7,13) 12343942084000822751.P56 92 (4) 34961.324599369.P79 93 (1,3,31) 237843323473654847623.P43 94 (2) 1693.6678701.181894150853.1823151514157.P63 95 (1,5,19) 125391374277955216479795494641.P46 96 (32) 2689.850177.7746049.13928006777524033.P35 97 (1) 3881.200924352971689432250644561.P71 98 (2,14) 197.33976720793233.P72 99 (1,3,9) L.M L (11L,33M) 95885659.166222146279939538766671 M (11M,33L) P32 100 (4,20) 401.2254601.5931105001.69084589801.P54 101 (1) 20201.228104057.1732951869588220873.P74 102 (2,6,34) 382645993638157.563620766036953.P38 103 (1) 1237.51396929137.3842537250772226605747.128288938117946418355541.P48 104 (8) 86759222313428390812218077095850708048977.P60 105 (1,3,5,7,15,21,35) 275310421.137031343051.P31 106 (2) 410982353.23746234974173.22250800656016001.72744498860303958101.P51 107 (1) 841021.P105 108 (4,12,36) 433.8209.P69 109 (1) 11119.14389.P105 110 (2,10,22) 1327481.36318547582241.110374378040081. .136371262802069831801.P30 111 (1,3,37) 37*.223.P72 112 (16) 10529.15233.132833.7782479531201887486913.P65 113 (1) 909877.P111 114 (2,6,38) 37820720459377.308673703543834165513.P41 115 (1,5,23) 2531.558956737278445325461.P68 116 (4) 233.287681.60604269272032563100609.1502477990708696255525449.P62 117 (1,3,9,13,39) P75 118 (2) 1291321673.1013563312793953470363741024001073. .64838817747578095323592827914385846481.P41 119 (1,7,17) 110917283.124214819.69796946717.256644509902201. .63063653308203311.2091456376138057349.315440418833726113081631 120 (8,24,40) 3121.114001.1698371041.12658046117876244394801.P27 121 (1,11L,11M) L.M L 727.1663628038071022183838437.P31 M 122453.2095721.103569468207767.P32 122 (2) 61*.733.15373.19042493.615339081285269009. .166945076296840267580084657135863728824204737.P47 123 (1,3,41) P84 124 (4) 1489.6449.11161.5721113.92247817.P100 125 (1,5,25) 251.559001.30877424283969568616368678353563069501.P59 126 (2,6,14,18,42) 2017.21673.1540217047797575204407748160801193.P35 127 (1) 509.2140352083. .4402640625848258016840688846660358437130425243742595514279.P62 128 2*.15361.111489577217.574341646346402207998363393. .4018529583345312964042058778793458689.P55 129 (1,3,43) 1291.P85 130 (2,10,26) 521.P98 131 (1) 9858799.119235724375228558113076040277225949839796708740043.P79 132 (4,12,44) 57563039928769.504278350263601.P55 133 (1,7,19) 23204027016899114504903.P91 134 (2) 47271776033.555596265747977.5653530366032833.P97 135 (1,3,5,9,15,27,45) 283771.861465705211.P58 136 (8) 17*.29584734433.P122 137 (1) 823.2467.12932527.666751384702583.33702237384570719055067.P91 138 (2,6,46) 277.6128029.P83 139 (1) 48560832383207.23835478071413231. .226911237770389320465096194749609274682969829.P70 140 (4,20,28) 281.7406965671094607547812305361.P70 141 (1,3,47) 2539.P93 142 (2) 192553.6896695512898403271082223952161993974407591311981.P92 143 (1,13) L.M L (11M) 859.2003.23167.36037.172626755159.619151422486169.P21 M (11L) 2008696691.303798181831.P43 144 (16,48) 3457.114500564929.P86 145 (1,5,29) 54521.P112 146 (2) 293.877.10851207624233. .1642924373932604240398418631306800170146224088997.P84 147 (1,3,7,21,49) 54447297367.593567588238393763.P59 148 (4) 1481. .10170146161160624507589185121238262249266667161256127057415217.P86 149 (1) 1193.1530827. .775322709138856254112793450158954494201167319485721463.P91 150 (2,6,10,30,50) 7884604271247668072701.P62 151 (1) 907.3323.255421785001.372781462691737543021989945244913.P106 152 (8) 13681.1077214649569.P134 153 (1,3,9,17,51) 2143.70740970147. .1840706193591427502373477305882643135847.P47 154 (2,14,22) 617.99793.28785963361.65808672978228777210147008368433.P75 155 (1,5,31) 25111.668671.1945899780650862081973056361. .25153949825237973485338723920570841.P54 156 (4,12,52) 1873.24337.332327331649.341226120551908708215217157918113.P49 157 (1) 424843.P157 158 (2) 21621681589.195687304237.2325820989287069. .2016628650692376508178693692448257. .177115854116776674014598663778398923878397.P51 159 (1,3,53) P109 160 (32) 225601.10628056841921.69220917578031208961.P96 161 (1,7,23) 1466711.6875023.18248063.2506937119. .75580484933767277650090124382122269.P73 162 (2,6,18,54) 793130293.P104 163 (1) 653.13693.5894172551186797.405880245798991364856121577.P120 164 (4) 13121.42641.2074273.7130393.40257849161.97352750991169. .2861311221613049.281713699327243441.552748497406807193.P70 165 (1,3,5,15) L.M L (11M,33L,55M) 331.3301.P37 M (11L,33M,55L) 3631.P38 166 (2) 4331273.24967511537.34960378781681173508155621. .2308531347471863958469313620650223778129.P89 167 (1) 1339169327. .3300432761858103866348058105008794336060997740879896086290505245157.P98 168 (8,24,56) 52081.126001.247437888847604652162337. .118738136976330434629762417.P41 169 (1,13) 3719.P159 170 (2,10,34) 3260777957463840456531891601.P106 171 (1,3,9,19,57) 395126219277461154409190377869979.P80 172 (4) 10321.895777.2291140793.4612466317049.18917231969257. .8993481304534541048526696863581326290994262879631297.P78 173 (1) 25218258782887.4657650196273780561.P148 174 (2,6,58) 12735009193.25405175682157.36144770810077. .9529369734426439596848326843374200197.P43 175 (1,5,7,25,35) 723451.28289718815384888394734507227024951.P85 176 (16) 35201.7434241.3035183032047230625631489.P131 177 (1,3,59) 709.8852479.418286047.29920690297. .4383533260821719783424892027.P65 178 (2) 46993.P179 179 (1) P186 180 (4,12,20,36,60) 554041634889835667266333598012061961.P65 181 (1) 1087.10499.28961.4928993.494599122567229. C155 182 (2,14,26) 2549.76872047790169633.603597442693160189. .21389858671812927839610150156529.P81 183 (1,3,61) 367.530733538977688353451.P102 184 (8) 5153.13249.3393866564381362044449.18762254284652611492897. .2178663038468353297718910823091125671985841.P90 185 (1,5,37) 13678726350491.510478568651306035780751621.P111 186 (2,6,62) 373.20089.323744320653227644676293. .387491950733013190146272614153.P65 187 (1,17) L.M L (11M) 1123.P80 M (11L) 1871.P81 188 (4) 149441953. C184 189 (1,3,7,9,21,27,63) 6427.41959.637438224833677. .652499617543540520675222321113591.P57 190 (2,10,38) 516262800270346286750957015107437143584755022581205411759884765761.P85 191 (1) 383.9295607545074385946753599. .10943652034918306516518686327929621233253.P131 192 (64) 4999681.188203763329.59825484896641.2522204187418753.P87 193 (1) 773.P198 194 (2) P200 195 (1,3,5,13,15,39,65) 1171.2159041.5347681.41711671.P77 196 (4,28) 4396564922913073.1000215069936448424297877519565769. .27584316197960616324036313486526262294434452581372529.P74 197 (1) C205 198 (2,6,18,22,66) 851401.4697405477458849.P104 199 (1) 8685953.146650663.3823602319.79365167307383.P168 200 (8,40) 90001.291281336764801.16625767615199325017280401. .896720806439075722628289609391420338234464212801.P75 201 (1,3,67) 3217.P134 202 (2) 3637.37442421086030953.P189 203 (1,7,29) 30061259593891.26317706159551360565552444185165409. .2393098526213023802467303772332124696379948606359.P79 204 (4,12,68) 21373370567867161.9389207830134041872135543904593.P86 205 (1,5,41) 35671.80519081.8240924561.19465938411835695151. .11970655810401989943242413896209071. .1118220897006993145148786216979797392760797171.P46 206 (2) C213 207 (1,3,9,23,69) 1575425458075847579018029.9430195587624521199783253.P89 208 (16) 5745664293565249. C185 209 (1,19) L.M L (11L) 397519.1304601827.5713257611105981119921.P58 M (11M) 419.48023563923633871.P75 210 (2,6,10,14,30,42,70) 4774799693782383634276354861375486612699501.P58 211 (1) 79842611423.24068102703304254483013.1274197670665384896310643.P162 212 (4) 20346651139084609. C201 213 (1,3,71) 1279.4261.38767.241314517.8698096969.14980015231. .146725989283141.61613677654149261712293660932063639173483.P52 214 (2) 715189.2220041882273434361683633. .167682147711592821398735713993001367086093.P150 215 (1,5,43) 813189004171.3197135804492492971. .193765176290056379756793725307814540891. .56621045460781648098610503847956528696245241991.P60 216 (8,24,72) 1297.6481.3182647681.13685944897.23652283000971422593. .1752300177786274178539088217518113.P71 217 (1,7,31) 241739.6151633335373.11105291873337733. .92128660012292036719950667586473.P122 218 (2) 15442249.90833189.343390549.13701517129. C192 219 (1,3,73) 3943.148483.13294559689.21149169451. .1227023342787622738230402973. .10554863204373603664496700868383796000277143.P51 220 (4,20,44) 881.23525041.2423799841. C147 221 (1,13,17) 443.15214967.P191 222 (2,6,74) 9499172909234906032067412079201033.P116 223 (1) 443686153.1140498656251.4147547632284793527095981801.P183 224 (32) 2758337. C194 225 (1,3,5,9,15,25,45,75) 906054085876149781651.P105 226 (2) 3617.228821837. C222 227 (1) 21549352320724159933.67332325557222369139.P197 228 (4,12,76) 430009.16460435892921560549676267982779313. .1530577370570695515843056744341672838593.P71 229 (1) P238 230 (2,10,46) 461.134445581.343290128859872186919542448578621. C140 231 (1,3,7,21) L.M L (11M,33L,77M) 463.1563791740201655119.P43 M (11L,33M,77L) 4621.6007.130958161489.41987897476328997733.P24 232 (8) 929.718243697.P222 233 (1) 467.47574407.1681082419.15300218543.2800063085689. C200 234 (2,6,18,26,78) 754417.P145 235 (1,5,47) 171956300431. C181 236 (4) 1245137.1820977.196612846857339161. .34640632020616953364419872758035731606321.C172 237 (1,3,79) 1298119153.442887255388335544085068774311818032069. .349848591222229454676083898046375211577130459.P71 238 (2,14,34) 18089.29125297186513714033.P177 239 (1) 63097.102293.57577969.13096317022627.1760573169194453.P202 240 (16,48,80) 3361.497281. .402968902472395360889178149434861784137338065281.P77 ------------------------------------------------------------------------------- 253 (1,23) L.M L (11M) 23*.34358491915519861.15081546136004856381787.P75 M (11L) 93792287513.1413086923931.P92 275 (1,5,25) L.M L (11L,55L) 109451.7669751.249327078001.1320705477851. .484953580035490730634734566779401.P37 M (11M,55M) 28948806319554206514033458668643493614401.P64 297 (1,3,9,27) L.M L (11M,33L,99M) 60212927509792800235219.5343727611107427419946338417467.P41 M (11L,33M,99L) 115564483.P86 319 (1,29) L.M L (11M) 126069439.54453236653277002250524018661761985258743661.P94 M (11L) 96937721.22395964041133.1674399383651611.24440702406360967. .4250822076554186563.1362428565267452997267408860021.P45 341 (1,31) L.M L (11M) 683.13751401821439225165451143629880111. .1012000371041933382912608396702713889156167.P77 M (11L) 88661.10766053.492922321.644552386633. .3454061988006506245928197.11635610293174280651716530998551.P69 363 (1,3,11L,11M,33L,33M) L.M L (121M) 2179.1213873.17156544164914857424669597171794606247.P68 M (121L) 4357.29698483.32054828257.22132988093371.P80 385 (1,5,7,35) L.M L (11L,55L,77L) 8939701.371071471.518583951271. .1048947375246657003170213161.P71 M (11M,55M,77M) 5487540521.3474031899426599281.P98 407 (1,37) L.M L (11L) 82262238908095416625629847487.P159 M (11M) 24421.368743.101730015473692321. .1583171273015273165687503920221.C130 429 (1,3,13,39) L.M L (11L,33M,143M) 349207.361219.P114 M (11M,33L,143L) 105121516501.80026964062240068874678393. .136781281056972929796341020181077888593676549.P45 451 (1,41) L.M L (11M) 2707.336017551.8911290961.1072881923818635144449927674819. .1815484843668506267988330171633365999003. .547152724762445363229755616341664505869098913767.P69 M (11L) 776075370379457963.8287290957329109961678200239527.P160 473 (1,43) L.M L (11L) 947.354751.744503.69716417. C197 M (11M) 8000323.368900269.38042842158630893.1285274840618548862537291. .57335965989876943599721563601.C134 11^{11h}+1=(11^h+1)L.M, L=A-B, M=A+B, h=2k-1, A=11^{5h}+5.11^{4h}-11^{3h}-11^{2h}+5.11^h+1, B=11^k(11^{4h}+11^{3h}-11^{2h}+11^h+1). Table 12- Factorizations of 12^n-1, n odd, n<240 n Prime Factors 1 11 3 (1) 157 5 (1) 22621 7 (1) 659.4943 9 (1,3) 37.80749 11 (1) 11*.23.266981089 13 (1) 477517.20369233 15 (1,3,5) 61.661.9781 17 (1) 2693651.74876782031 19 (1) 29043636306420266077 21 (1,3,7) 8177824843189 23 (1) 47.39891250417.321218438243 25 (1,5) 303551.12629757106815551 27 (1,3,9) 306829.86769286104133 29 (1) 59.24767.368939.3335672988472972523 31 (1) 373.126883621.23364027983.234187563803 33 (1,3,11) 886381.5999137.661269577 35 (1,5,7) 71.491.806821.6089651.425455031 37 (1) 3933841.196560666553286126588980353347341 39 (1,3,13) 36973.17654521.111704871987697 41 (1) 83.1977898057.97668924760419986491370101198871 43 (1) 431.12313309.13444466603.32359758358562524963364461 45 (1,3,5,9,15) 30781.5234401.21456901.22981681 47 (1) 10617249990997021.4509348865973648037702008076799297 49 (1,7) 77617.27268138641564464649627762762033543154129 51 (1,3,17) 20757613.1510376787258214230993801577 53 (1) 107.743.1694941.29504677.3089222210773.11639817348279944053139101 55 (1,5,11) 5281.442434513819541.5766308324790114380136001 57 (1,3,19) 114001.129733.20526705689989.2141456811167917 59 (1) 22067.33565608845417661253.576319092656266231937955277485160608227 61 (1) 1706293.1000831393.35995548461449237368649937465097120608531155491049 63 (1,3,7,9,21) 708391688852136898302887193094373767489 65 (1,5,13) 131.1932288541.596827590710414051.38346067178495390031121 67 (1) 45464593.16180787699.17577834702049211.P38 69 (1,3,23) 6279903241741823809.P29 71 (1) 5113.19597.P68 73 (1) 50654608967364071.P62 75 (1,3,5,15,25) 601.80342401.P33 77 (1,7,11) 4621.379101493.191199728567.50565974802015289.P25 79 (1) 162109.130479719.P71 81 (1,3,9,27) 5937949.660198074631409.P37 83 (1) 167.997.1993.22079.557889481.35238620437.2731547200091. .10052468384786123.P28 85 (1,5,17) 1021.22271.4832761.204560684821.5383015065849288291601.P22 87 (1,3,29) 349.1741.74233562929.936727604123432773.P26 89 (1) 179.2137.120863.3163346581.16649789224075621. .35035317869663569.255053775727906405559.4656868283889935515079 91 (1,7,13) 152705150363039.1091317880778743355464526983.P37 93 (1,3,31) 8929.1261081.16185865453.P45 95 (1,5,19) 191.P76 97 (1) P104 99 (1,3,9,11,33) 397.3169.9143902271574719666671109149.P31 101 (1) 20359133179252403.P92 103 (1) 3709.7417.1309643353.13951770188639477959439. .226319692803146344014357964333823.P40 105 (1,3,5,7,15,21,35) 2521.126001.9562853581.P34 107 (1) 126047.8368183883.P100 109 (1) P117 111 (1,3,37) P78 113 (1) 227.7450459827983.316093109705519.753692779085581623227.P71 115 (1,5,23) 2531.P92 117 (1,3,9,13,39) 6553.774101091754693.5363939350752581033772013.P35 119 (1,7,17) 239.1429.137089.23082431.P86 121 (1,11) 11*.7019.9971358563.13448069471. .36801041190212623908408703917306494049155113.P51 123 (1,3,41) P87 125 (1,5,25) 251.13751.118751.P97 127 (1) 88750555799.2597995311343175210111334225450311.P92 129 (1,3,43) 3784861.P85 131 (1) 263.P138 133 (1,7,19) 67033.365876351.153373238287849222871747653.P77 135 (1,3,5,9,15,27,45) 11719914497486992163161.45726761961907655567941.P33 137 (1) 7894763.99485649955791433. .4270306101158898662140485488376974936909627.P81 139 (1) 32830711631.149723271154501574581. .13976446202665769757077661403698383112061728500003.P70 141 (1,3,47) 3504133.5136890928835357.P77 143 (1,11,13) 1068975337.28151299084766629509889009.P95 145 (1,5,29) 8458141.152107892171.2833016858862791.P88 147 (1,3,7,21,49) 7622826121.3053140047080689861. .29014061524726574502110353.P37 149 (1) 11027.1919442572897362836803025134228929025089.P117 151 (1) 16537237851564688924261407041648853990657743.P119 153 (1,3,9,17,51) 613.3673.6128894197.1644982406845777. .216486853727393579797.53294740218449478902707453.P27 155 (1,5,31) 311.17379312247321.32179535439223966162981. .504159451473002560362013386812584959284471.P50 157 (1) 3769.896587135133828036528709133.P138 159 (1,3,53) 30529.526468081.564397849.P91 161 (1,7,23) 1933.36709.8820656418738378259508980670038453.P101 163 (1) 3123955328977664272236491.3085088915212385601857770168909. .55276244920832349213682617306044898442152509401.P74 165 (1,3,5,11,15,33,55) 475350812105401.P72 167 (1) 553194672940916339.P162 169 (1,13) 273854127119.42085870270393.171074557867837392887. .2236719302927635268499980471.P96 171 (1,3,9,19,57) 2053.25309.P109 173 (1) 347.6229.178537.16520618724247316579377. C152 175 (1,5,7,25,35) 2453984000813135412614651.P106 177 (1,3,59) 6373.472683457.29664964237.48253224577.215006774581. .2245657505577169.247679421927970902164473.P42 179 (1) 359. C190 181 (1) 56473.188954578048573195547226930925499.P158 183 (1,3,61) 7321.7756968162619561.P110 185 (1,5,37) 6441085856120368040593352248224844221696350548901425367127551.P95 187 (1,11,17) 7824829.6367170107.5272292087965614119.P138 189 (1,3,7,9,21,27,63) P117 191 (1) 383.2293.5576463887.492394777262152830140779120613620261.P154 193 (1) 6563.143593. C199 195 (1,3,5,13,15,39,65) 24263325716698381.457644272256236018195571421.P61 197 (1) C212 199 (1) 11941.50445745393.534989935052173.452633703528239603. .2408107039243923308111.C146 201 (1,3,67) 492853.337362557588033581. .2340033136012362062475950746729856638028655463932144793.P65 203 (1,7,29) 2437.2032540343.168010120865329. .4038644506148119439397242761.P127 205 (1,5,41) 50860501.61708179551.109423722071.594458960231.1272168094511. .59114755745455413432518951.802612658538701099788630604070125125897621.P52 207 (1,3,9,23,69) 123373.46359329929201.80965151313250177.P107 209 (1,11,19) 419.167246399.19043506626213169.2877972269567413524001. .131258359076578876173923.4714073727036453202094931887.P95 211 (1) 98327.599663.8960574127139.1374686882866127. .11442157099782185036780447859311.C157 213 (1,3,71) 853.668821.5938441.14726274721.593597578469053.P111 215 (1,5,43) C182 217 (1,7,31) 5077606871.30847829203283.3621684771405978346406298479029.P141 219 (1,3,73) 877.384229369.13036824921402558973.P125 221 (1,13,17) 443.9640021.52016377765223.141523296304179193. .27267433046893619404631197.2767487366128813243478189568387004020073.P102 223 (1) 1423187.23385119.14130288853.43954882455277. .1006249991892868346686216789.P176 225 (1,3,5,9,15,25,45,75) 2363726892633483756321124302681778344117301.P88 227 (1) 147551.256057.152574419.1267583437.110565744056955405733. C197 229 (1) 76487. C242 231 (1,3,7,11,21,33,77) 793717.1053467722693.237808105253287801. .1285249260419549776349461.P71 233 (1) 467.31223.78863682072342587129533815443. C215 235 (1,5,47) 4982941.11664037157021516682204241. C167 237 (1,3,79) 6637.114598432057.1286930998217149714369. .27567862476721705741499814127507129428735247904137980751231873.P71 239 (1) 479. C255 Table 12+ Factorizations of 12^n+1, n<=240 L,M for n=6k-3<=477 n Prime Factors 1 13 2 5.29 3 (1) L.M L 7 M 19 4 89.233 5 (1) 19141 6 (2) 20593 7 (1) 211.13063 8 17.97.260753 9 (1,3L,3M) L.M L 1657 M 1801 10 (2) 5*.85403261 11 (1) 57154490053 12 (4) 193.2227777 13 (1) 13*.79.36037.222379 14 (2) 673.13156924369 15 (1,5) L.M L (3M) 31.421 M (3L) 35671 16 153953.1200913648289 17 (1) 2551.66900193189411 18 (2,6) 73.122138321401 19 (1) 3307.8209.905265296671 20 (4) 41.521.127921.67657441 21 (1,7) L.M L (3M) 1885339 M (3L) 7*.43.17011 22 (2) 2377.3697.6337.68368660537 23 (1) 829.12421.49489630860836437 24 (8) 7681.40609.592734049 25 (1,5) 1951.60601.73951.438472201 26 (2) 53.677.2200289654266792155913 27 (1,3L,3M,9L,9M) L.M L 109.47336293 M 271.487.39097 28 (4) 79493013628273739882868481 29 (1) 1402596253.1084876017544880450377 30 (2,6,10) 186168115009253521 31 (1) 1263499.173420475484059478781201647 32 769.44450180997616192602560262634753 33 (1,11) L.M L (3L) 67.199.1453.5479 M (3M) 39105782299 34 (2) 79471453801.427152748915310957418697 35 (1,5,7) 86121235964912696227980301 36 (4,12) 2231857.3684845809.9666387937 37 (1) 5250079.4150805645839.30023720899326796981 38 (2) 1977673.176477034940417.2016864235215616489 39 (1,13) L.M L (3L) 859.17793645013 M (3M) 313.17991125491 40 (8) 34182189107670005092862256297738241 41 (1) 12301.1684652527.13657436942593.47936660465075191 42 (2,6,14) 80048881834094656438235281 43 (1) 71209.372060253.10273420681.7177727914895266742809 44 (4) 67651673.217245283970973197278039678825711337 45 (1,3L,3M,5,15L,15M) L.M L (9M) 181.47263556341 M (9L) 9298142299081 46 (2) 302669957628317561107372328495588758678132736113 47 (1) 18049.12349627.21622395121.8405516927437711741762092271 48 (16) 7489.3122881.1461573322938242802306049 49 (1,7) 8356734198817312279063.253265324522131745115559 50 (2,10) 5*.101.1201.700936801.2334798291701.14807687049800501 51 (1,17) L.M L (3M) 307.380355066717049 M (3L) 103.3077130526103089 52 (4) 288913.25265657.865727447657645665290857439836665912121 53 (1) 3181.33073.77366539.14861828970617714166257633556559606415803 54 (2,6,18) 433.3889.42729553.165042892009.59686188135337 55 (1,5,11) 331.6271.164018234982236911.46768482029635739671 56 (8) 113.2129.244721.527633.22232950788588289.9150512297530943809 57 (1,19) L.M L (3M) 19*.884986147755302617 M (3L) 229.62701.3178598581687 58 (2) 29*.1277.378509.9533379150437.507127415651053993.39821279284774257217 59 (1) 709.1063.25232402089.21271304642628211.892931082048097905588129990661 60 (4,12,20) 241.141841649932724596178535977341201 61 (1) 111997.7361466337.5188602220069.P38 62 (2) 617521.26825115448057.87873272984241400393.P26 63 (1,3L,3M,7,21L,21M) L.M L (9M) 127.79277059.2537121133 M (9L) 27764103747580691401 64 36097.81281.69619841.73389730593973249.P35 65 (1,5,13) 37831.52960051.P40 66 (2,6,22) 109297.219649.1717321.P27 67 (1) 44623.2291803.P61 68 (4) 137.17019338113.P57 69 (1,23) L.M L (3L) 139.277.8419.22542577.129512587 M (3M) 348670382471247108491803 70 (2,10,14) 71874601.10365509281.1612092376073761.5298455664688950121 71 (1) 48058613330617.P62 72 (8,24) 577.2752993.15670947324691873.P27 73 (1) 439.346059859.6325722879776491.P51 74 (2) 149.48989.417509.21617621.13721476576343266613693.P36 75 (1,5,25) L.M L (3L,15M) 151.2251.1696501.6625387201 M (3M,15L) 395251.9733315100252251 76 (4) 7889080897.143529155542303647618953713.P42 77 (1,7,11) 463.P63 78 (2,6,26) 3247609.23709901801.P35 79 (1) 5434599708664429598203.270354982362100782692527.P39 80 (16) 2081.2478806527025281.214538593513800809975201.P28 81 (1,3L,3M,9L,9M,27L,27M) L.M L 163.811.1621.641065152502677063709 M P30 82 (2) P87 83 (1) 499.8305623819547.5277826961453441457872455753.P46 84 (4,12,28) 337.10753.284065793761.P34 85 (1,5,17) 235111.32182021.182593435609480192119451.P33 86 (2) 173.195049.1260760517.247819688992536197.881572852017880141483757.P33 87 (1,29) L.M L (3M) P31 M (3L) 2032959451.1390046661396154093141 88 (8) 2481601.6188868577.49514757601.8200539405448794297995729.P35 89 (1) 7477.572511347126394968679427.P68 90 (2,6,10,18,30) 1653489395093881.33276147172349761.114859125525232035721 91 (1,7,13) 1093.44773.2322926580703.2620222710234691381.P40 92 (4) 23369.36433.44805941084686008411833430562841.P55 93 (1,31) L.M L (3M) 5209.24221034391.1188277798029874021 M (3L) P33 94 (2) 941.1129.6581.56078144420933.1645156433564398201. .19141017664453895628642529.P33 95 (1,5,19) 251831088886489381.P61 96 (32) 1153.2689.4993.22273.3124609.3531754753.P39 97 (1) 322429.P99 98 (2,14) 197.81667460066590930293917.P66 99 (1,3L,3M,11,33L,33M) L.M L (9L) 5690162377645219.43504476926662819 M (9M) 2971.P29 100 (4,20) 15601.55201.9880627023929801.P62 101 (1) 1213.21211.P101 102 (2,6,34) 409.615782161.P58 103 (1) 1237.289765369.1003041977479.13561251678157.987452638049443. .237720321284227801429.P38 104 (8) 3946177.235590161.2394253229201412644716539488455823024969393.P47 105 (1,5,7,35) L.M L (3L,15M,21M) P26 M 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333 (1,3L,3M,37,111L,111M) L.M L (9L) 124543.119810607463.615366154824465215271421.P77 M (9M) 47287.71263.2616651769743883.P92 339 (1,113) L.M L (3M) 764110694773033.73282934361847577401.1147032708195514473009031.P62 M (3L) 2793740569392459675945343.P97 345 (1,5,23,115) L.M L (3M,15L,69M) 691.24581965534907417117282311.P67 M (3L,15M,69L) 96801166741.4912523136523783944565190673920491013101.P45 351 (1,3L,3M,9L,9M,13,39L,39M,117L,117M) L.M L (27L) 17551.129169.314132679901.17719478069541690622753. .501073941779111566528388153767.P44 M (27M) 18253.10182380153167.5557307465977957.1287078033734511273919.P63 357 (1,7,17,119) L.M L (3L,21M,51M) 595588813.53179121411533282455104389. .7444967386325111267663723410113529.P35 M (3M,21L,51L) 3571.8895013.26108923931329.1485478883324335621849.P59 363 (1,11,121) L.M L (3L,33L) 11617.1902847.4240567.233011560739. .17590776403036520999000083528813789198205653.P48 M (3M,33M) 2179.116574547.P108 369 (1,3L,3M,41,123L,123M) L.M L (9M) 739.136531.3642031.5752711.1423355095922941. .374072153370327840457698722983.P64 M (9L) 14627161.105843637766088877609. .3270052699297600797400421230129564000055047.P60 375 (1,5,25,125) L.M L (3M,15L,75M) 862768857355002751.26061802206090827529591526287333751.P56 M (3L,15M,75L) 751.1861999501.P96 381 (1,127) L.M L (3M) 1524763.12721529803.206375981018136378198643. .22179455009646313890461937208319215171.P59 M (3L) 2287.970789.409795207580354851.1480444859343993091644952608883. .1140932738223148258864544522278327.P47 387 (1,3L,3M,43,129L,129M) L.M L (9M) 6967.4388268096716033913973672130408161496791. .202923202077686203277513231859003158873473.P52 M (9L) 5419.34057.51859.607848517.11281513627.169315811495745796632187.P81 393 (1,131) L.M L (3L) 787.288931243.7853352071229031. .3540037548679408652606516870379751.P80 M (3M) 47161.540200509.173461409377.P116 399 (1,7,19,133) L.M L (3L,21M,57M) 7928131.1262555546640315313.P92 M (3M,21L,57L) 332767.17706929602633139191.1062177777127068280484149.P68 405 (1,3L,3M,5,9L,9M,15L,15M,27L,27M,45L,45M,135L,135M) L.M L (81M) 171947421803819953791091.500131074548916716314179353131.P64 M (81L) 9230674951.P107 411 (1,137) L.M L (3M) 32059.88630068743448247758082010402431935794978004066530299.P90 M (3L) 139729711658022289818417409915604887567.P109 417 (1,139) L.M L (3M) 1669.15013.110923.208501. .5638888896763019486450225237314251285030538064074261.P80 M (3L) 3964837.P143 423 (1,3L,3M,47,141L,141M) L.M L (9L) 103169155868277226048549.10455277041391964392381265548669243. .381846165419473573914787041977491293397073551.P48 M (9M) 554977. .49428368266998575771508427851382501624434884685008412777493.P85 429 (1,11,13,143) L.M L (3L,33L,39L) 3729230661964237.P114 M (3M,33M,39M) 274233961.593967524131726603.159504077463298584589. .43450210975084947437977.P61 435 (1,5,29,145) L.M L (3L,15M,87M) 69872836351.887257418543475083551.P89 M (3M,15L,87L) 3628562344662781538711332722241635752511217245360661.P70 441 (1,3L,3M,7,21L,21M,49,147L,147M) L.M L (9L,63M) 3529.11467.69710998267.162145535833.1208862422525899.P92 M (9M,63L) 47629.312229.3819943.147915811.400268955783439. .80563595863991546010661115881806884967004027.P53 447 (1,149) L.M L (3M) 242685942045674495792268869293516616521379017039547818607\ 03146532721181.P90 M (3L) 13411.3740497.27760489. .2085436050830101868627222971448078347771532442559785477511.P85 453 (1,151) L.M L (3M) 7345054738129351972681432555641148061413364808769116545344488307.P98 M (3L) 1348129.2092861.112341266088109835884435114483. .3206046355269404360980173532840459.7154409726952489428326850247389343.P54 459 (1,3L,3M,9L,9M,17,51L,51M,153L,153M) L.M L (27M) 6427.8263.3290873941. .4772949043296938327540555652344566627901623072447285275681332599.P75 M (27L) 2583416323.1848577259045898983521.P125 465 (1,5,31,155) L.M L (3L,15M,93M) 33661195621.7608436297012031616889789008167761321.P82 M (3M,15L,93L) 31*.4853358451.P119 471 (1,157) L.M L (3L) 44704452965167992989021059. .3373910943552318560566312255270898933180978334214232817297798982057.P77 M (3M) 7537.15073.12453241.35010373.74479461399093993433. .31289406059597855950513457417424955206259.P86 477 (1,3L,3M,53,159L,159M) L.M L (9M) P169 M (9L) 6679.126563242535798869117.121272451003595655053743013354\ 36857963786417904384880169071412408713919.P75 12^{3h}+1=(12^h+1)L.M, L=12^h-2^h.3^k+1, M=12^h+2^h.3^k+1, h=2k-1.