From: mathwft@math.canterbury.ac.nz (Bill Taylor) Subject: An odd perfect number? Date: 1 Apr 1999 03:28:52 GMT Newsgroups: sci.math Keywords: Almost :-) Descartes discovered this... 2 2 2 2 Let n = 198585576189 = 3 .7 .11 .13 .22021 2 2 2 2 Then (1+3+3 ).(1+7+7 ).(1+11+11 ).(1+13+13 ).(1+22021) = 13.57.133.183.22022 = 397171152378 = 2.n (!) So it looks like n might be an odd perfect number! Alas, 22021 is not prime, so the last factor is not of the correct form. Pity. But we might perhaps say... "If 22021 were prime, then n would be an odd perfect number." ========================================================== How's THAT for a counter-factual conditional! ------- Hmmmm... hey, wait a minute though... if 22021 *were* prime, then maybe the multiplicands wouldn't multiply up to include 22021 in the 2n product. Hmm. Maybe these quantum physicists are right after all, not to countenance counterfactual conditionals as having any meaning. --------------------------------------------------------------------------- Bill Taylor W.Taylor@math.canterbury.ac.nz --------------------------------------------------------------------------- Every problem has at least one solution which is elegant, neat - and wrong. ---------------------------------------------------------------------------