Thanks for the "p-1 for dummies" e-mail.
Starting from this definition of the "p-1" method (I changed p to q).
Discover prime factors q of a given large (mersenne) number N,
when all prime factors of q-1 are "small".
But as everyone on this list knows, any factor of a Mersenne
number looks like 2*k*p+1 for N=2^p-1. Plugging this into
the above equation gives
q=2*k*p+1
q-1=2*k*p
(It has been too many years since my last math class, so go easy OK?)
Doesn't this mean the lower bound on a "p-1" method search should
be greater that the Mersenne exponent (the p in 2^p-1) to have the best
chance of success? Then the "upper bound" of the "p-1" search can
be resevered for cracking a big factor in the "k" of a Mersenne factor.
Brian Beuning
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