If I understand P-1 factoring correctly, then using it to a stage one
bound of k to try to factor M(p) will find all possible factors less
than or equal to 2*k*p + 1. I'm assuming that p is less than k (or p
is always used in the powering) and the convention several of us
agreed on a while back that all prime powers less than the stage one
bound are used in the powering, not just the primes themselves. That
is, trying to factor M(97), say, to a stage one bound of 10 would use
8, 9, 5, 7, and 97, not just 2, 3, 5, and 7.
Am I correct? Or could a factor smaller than 2*k*p + 1 be missed in
some cases?
Does it matter whether p is prime or not? I don't think so, but ...
This is not idle curiousity; I want to use this knowledge to shrink
some known trial factoring gaps in the data that I maintain, and this
would reduce them substantially. Actually, the gaps are only in data
for prime exponents, so that the one question above _is_ idle
curiousity.:)
Thanks,
Will
http://www.garlic.com/~wedgingt/mersenne.html
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