Quote:
Originally Posted by cheesehead
My understanding is that, in the Prime95 implementation of the P1 algorithm, b1 is the upper limit on the prime 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 prime factor of k is less than (or equal to, if b1 were prime itself) 10000.

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.)