Re: Mersenne: A couple quick questions

[Hans-Martin Anger]

let m=2^(a*b)-1.
then 2^a-1 is a divisor of m.

example:
2^35-1=(2^5-1)*(2^30+2^25+2^20+2^15+2^10+2^5+1)

general:

2^(a*b)-1 = (2^a-1)*(2^((b-1)*a)+2^((b-2)*a)+...+2^(1*a)+1)

regards
Martin

-Ursprüngliche Nachricht-
Von: Nathan Russell [EMAIL PROTECTED]
An: [EMAIL PROTECTED]
Gesendet: Samstag, 26. Februar 2000 06:33
Betreff: Mersenne: A couple quick questions


 I just joined GIMPS (now 6% done testing a number with exponent just
 short of 10M if it makes a difference) and I have been looking into the
 theory behind Mersenne primes.
 Can anyone show me or at least point me to a webpage with the proof
that
 the exponent of a Mersenne prime must be prime.
 snip ===


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Re: Mersenne: Factoring beyond ECM

[Hans-Martin Anger]

LiDIA is a free package for long number arithmetic.
It includes a demo-program for factoring numbers with trial factoring, ECM
and MPQS successive.
See here: http://www.informatik.tu-darmstadt.de/TI/LiDIA/Welcome.html

regards
Martin


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Von: Foghorn Leghorn [EMAIL PROTECTED]
An: [EMAIL PROTECTED]
Gesendet: Samstag, 22. Januar 2000 23:24
Betreff: Mersenne: Factoring beyond ECM


 I'm interested in trying to factor composite numbers with 100 to 200
 digits. ECM becomes impractical for numbers without any factors below
 50 digits or so. I have heard of algorithms such as MPQS which are
 used to tackle larger numbers. Are there any (preferably free)
 implementations of this method (or another) that would be feasible to
 run on a home PC or Unix workstations?

 Foghorn Leghorn
 [EMAIL PROTECTED]
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