From: rusin@shavano.math.niu.edu (Dave Rusin) Subject: Re: Primes in arithmetic sequence Date: 14 Jun 1999 22:53:06 GMT Newsgroups: sci.math Keywords: primes in arithmetic progression, consecutive primes in a.p. In article <7k355r$p3j$1@sparky.wolfe.net>, Jon Cosby wrote: >If anybody's interested, I'm attaching a table of 4-term sequences and their >gaps (what's with the sixes?) up to one million. There are no 5-term >sequences; can anybody think why this would be? Maybe I just need to choose >a higher number, but I've already spent enough time on this. Oh, longer sequences of primes in A.P. are certainly known. I don't remember the latest record, but in Guy's "Unsolved Problems in Number Theory" section A5 discusses long sequences of primes in A.P.; for example there are 12 primes starting with 23143 and common difference 30030, and sequences of 21 primes are listed. These progressions skip over some intermediate primes, but need not. E.g. about a year ago Dubner, Forbes, et al. reported a set of ten _consecutive_ primes in A.P.; see e.g. http://forum.swarthmore.edu/epigone/sci.math.research/phiskonthand from which I draw the excerpt, "...ten consecutive primes P, P+210, P+420, P+630, P+840, P+1050, P+1260, P+1470, P+1680 and P+1890, where P = 507618446770482*m + x, the first of the sequence, is the 92-digit number 100 99697 24697 14247 63778 66555 87969 84032 95093 24689 19004 18036 03417 75890 43417 03348 88215 90672 29719 " So you see you just had to go a little further. :-) dave