Originally Posted by cheesehead
Correction:
My understanding is that, in the Prime95 implementation of the P1 algorithm, b1 is the upper limit on the powerofaprime factors of the "k" of potential factors 2kp+1 of 2^{p}1 that are to be found by the P1 method.
That is, stage 1 P1 with b1 = 10000 performed on 2^{p}1 will find any factor 2kp+1 of 2^{p}1 in which the largest powerofaprime factor of k is less than (or equal to, if b1 were prime itself) 10000.
Example:
59704785388637019242567 is a factor of 2^{6049993}  1.
59704785388637019242567 = 2 * 4934285493275531 * 6049993 + 1.
Prime95's P1 stage 1 with b1 = 4000 would find this factor because the largest primepower factor of 4934285493275531 is less than 4000.
4934285493275531 = 61^{2} * 593 * 983 * 1153 × 1973.
61^{2} = 3721.
In this example the factor 59704785388637019242567 could have been found in stage 1 with b1 as low as 3721.
Also, Prime95's P1 stage 2 with b1 = 2000 and b2 = 4000 would find this factor because the largest primepower factor of 4934285493275531 is less than 4000 and all other primepower factors are less than 2000. (In fact, b1/b2 as low as b1 = 1973, b2 = 3721 would have worked.)
