>From: "Alexey Guzeev" <[EMAIL PROTECTED]> >Date: Tue, 12 Jan 99 08:30:42 -0500 >Subject: Mersenne: Factoring > > Ok, George's programs looks for only for factors of M(n) in form >1) 2kn+1 > that's clear why >2) 1,7,17,23,31,41,47,49,71,73,79,89,97,103,113,or 119 modulo 120 > but this is not. Why factors 120k+13 are not considered? Or 120k+19? Why only those 16 reminders of >~30 primes below 120? Because a separate theorem tells us that factors of Mersenne primes must be 1 or 7 modulo 8 (because 2 must be a quadratic residue. The argument is simple, but I learnt it carefully for Finals and have now forgotten it).
