mersenneforum.org B1/B2 values
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 2012-11-12, 06:42 #1 esakertt   Oct 2012 B16 Posts B1/B2 values In exponent info link, some B1/B2 values are shown for some exponents (P-1 tests). Without knowing about the P-1 tests and the theory behind them, I would ask how to use this B1/B2 information before the LL test ? Why this B1/B2 info is given ? I have not studied the P-1 tests.
 2012-11-12, 07:11 #2 Dubslow Basketry That Evening!     "Bunslow the Bold" Jun 2011 40
2012-11-14, 13:11   #3
esakertt

Oct 2012

11 Posts

Quote:
 Originally Posted by Dubslow P-1 is an algorithm to attempt to factor a number. In order to understand P-1, you need to understand smoothness of a number. That is, a number is n-smooth if all its prime factors are less than n. 100 is 5-smooth, as an example. In order for P-1 to find a factor p of a number N, p-1 must be sufficiently smooth. Specifically, if p-1 is B1-smooth*, then the P-1 algorithm will find that p is a nontrivial factor of N. (Actually, all prime factors of of p-1 must be less than B1, with one exception; the one exception must be less than B2.) The higher the bounds, the more likely it is that p-1 is B1/B2-smooth, and thus the more likely it is to find a factor, but of course it also takes more work. Prime95 has a somewhat sophisticated algorithm to determine the bounds that have the most chance to find a factor per work done. To be clear, B1 and B2 do not affect the LL test directly; the only correlation is, the higher B1/B2 are, the more likely that P-1 run was to find a factor. (*Actually actually, p-1 must be B1-powersmooth, not just B1-smooth. That is, all prime powers of p-1 must be less than B1; as an example, 100 = 2^2 * 5^2 is not 5-[/i]power[/i]smooth but is 25-powersmooth.)
Thanks very much.

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