> I've been reading up on the P-1 method ... am I missing something?
I don't think so, except perhaps for on possibility...
>
> 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 believe, or at least sincerely hope, that the text is incomplete. Every
implementation of P-1 of which I'm aware which is to be used to factor
integers whose factors are known to be of the form kp-1 invariably throw in
an additional k, as well as all the prime powers up to the B1 limit. (And
likewise for P+1 and factors of the from kp+1).
If the text is not incomplete, someone fix the program!
Paul
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