I've been reading up on the P-1 method ... am I missing something?
For a Mersenne number 2^n-1 with n prime we know that all the factors
are of the form 2kn+1 for some integer k. So the factorization of p-1
_must_ include at least one factor equal to n.
But the text leads me to believe that the P-1 method will only find
factors when the factorization of P-1 contains no primes greater than
the search limit.
So, is using P-1 to factor Mersenne numbers with exponents in the
millions but with B1 ~ 60,000 and B2 ~ 720,000 doomed to failure, or
is my interpretation of the text completely wrong?
I am (as an experiment) currently running P-1 on 2^11692589-1 using
B1=60000 and B2=720000. I happen to know that 5318756664776903 ( =
2*k*11692589+1 for the prime k = 227441359) is a factor of this
number, it will be interesting to see if P-1 finds it. Trial
factoring will find this particular factor quite quickly!
Regards
Brian Beesley
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