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

Reply via email to