On Wednesday 04 January 2006 15:23, John R Pierce wrote: > alpt says they've been having problems mailing to the list,
I haven't had problems recently... > -------- Original Message -------- > > >From [EMAIL PROTECTED] Tue Jan 3 07:57:33 2006 > > Date: Tue, 3 Jan 2006 07:57:33 +0100 > From: Alpt <[EMAIL PROTECTED]> > To: [email protected] > Subject: Mrepfact: a simple way to factor a Mersenne number > > I don't know if this can help you guys, > but maybe yes ^_^. Mersenne numbers with non-prime exponents are of limited interest to the project (well, me anyway) as all of them are composite. A few lines of algebra is sufficient to establish this. There is a major difference between finding a factor of a (prime exponent) Mersenne number and proving it composite since a factor can be checked directly with a very, very small amount of computation compared with the amount of number crunching required to check the result of a LL test. What would be interesting is an algebraic method of constructing factors for at least some classes of prime-exponent Mersenne numbers. The only one I'm aware of at present is: If p is a prime such that p+1 is divisible by 4 and 2p+1 is also prime, then 2^p-1 is divisible by 2p+1. If we could establish a set of relationships of this type, then we might save a significant amount of effort by eliminating exponents without even going to the trouble of trial factoring. [The relationship we do have is actually almost useless as the factor will be the very first checked during trial factoring!] Regards Brian Beesley _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
