> 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
Correct.
> 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.
No. Simply multiply the exponent on the base by p. This produces the
desired result, without having to go to the extra effort of extending the
bound that far.
I probably should add a section on P-1 to the FAQ.
-Lucas
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