> I was just wondering, could anyone give me any info on how factoring is
> done, is there a preliminary factoring before numbers send out, how high
> we factor, what possible factors are, etc. and also, I would really like
> to see the maths behind it as well. I need something to study over summmer
> vac :)
Well, the two biggies are that factors of 2^p-1 (for prime p)
must be of the form 2*k*p+1, and such factors must be be congruent to
1 or -1 (7) mod 8,
(or in other words) they must be of the form
8*n+1, or 8*n-1.
For proofs (I don't have time right now :( ), see
http://www.utm.edu/research/primes,
and look at the section on mersenne numbers.
Also, you can find a marvelous discussion in the archives for this list.
-Lucas Wiman
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