Thread: P-1 question
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Old 2011-10-07, 11:34   #4
Mr. P-1
 
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Jun 2003

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Quote:
Originally Posted by Bdot View Post
Can someone please explain why P-1 was able to find this factor?
Check your results.txt file. If you see the parameter E=6 (or some higher number) in the status line, then the Brent-Suyama extension to stage 2 was used, which will occasionally find a factor with one prime factor of k > B2 and all others < B1. This optimisation requires additional memory, so it is not usually in effect unless the available memory is particularly generous.

There are other possibilities, even without the the B-S extension. The Stage 2 code uses an optimisation called prime pairing, which sometimes includes two primes between B1 and B2 per iteration, instead of the one per iteration that a naive implementation would do. This is primarily a speed-up - you need fewer iterations to include all the primes - but it does have a potentially beneficial side-effect: Stage 2 can find a factor whose k has two prime factors between B1 and B2 if those primes happen to be paired. The likelihood is small, and I have never heard of such a case.

With the B-S extension there are yet further possibilities, such as Stage 2 finding a factor whose k has one prime factor between B1 and B2 and one > B2, or more than two > B1. The likelihood is even smaller, and again I have never heard of such a discovery.
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