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Old 2016-06-19, 19:29   #45
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Sep 2003

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Originally Posted by axn View Post
Obviously, this doesn't involve factoring the composite factor's k -- that part is very much useless.
It's not entirely useless.

Every factor of a Mersenne number is of the form q = 2kp + 1, so q−1 = 2kp. Here "q" is the "P" of the P−1 factorization method, so displaying the factorization of k tells you at a glance how powersmooth q−1 is.

You can see at a glance (after the fact, of course) what the smallest bounds of B1 and B2 would have been for finding that factor with the P−1 method. So you could often distinguish at a glance how likely it was that the factor was found with P−1, as opposed to ECM or TF.
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