20121112, 06:42  #1 
Oct 2012
B_{16} Posts 
B1/B2 values
In exponent info link, some B1/B2 values are shown for some exponents (P1 tests). Without knowing about the P1 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 P1 tests.

20121112, 07:11  #2 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
1110000110101_{2} Posts 
P1 is an algorithm to attempt to factor a number.
In order to understand P1, you need to understand smoothness of a number. That is, a number is nsmooth if all its prime factors are less than n. 100 is 5smooth, as an example. In order for P1 to find a factor p of a number N, p1 must be sufficiently smooth. Specifically, if p1 is B1smooth*, then the P1 algorithm will find that p is a nontrivial factor of N. (Actually, all prime factors of of p1 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 p1 is B1/B2smooth, 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 P1 run was to find a factor. (*Actually actually, p1 must be B1powersmooth, not just B1smooth. That is, all prime powers of p1 must be less than B1; as an example, 100 = 2^2 * 5^2 is not 5[/i]power[/i]smooth but is 25powersmooth.) Last fiddled with by Dubslow on 20121112 at 07:13 Reason: formatting 
20121114, 13:11  #3  
Oct 2012
11 Posts 
Quote:


Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Timing for different B1 values?  CRGreathouse  GMPECM  8  20180512 05:57 
Erroneous values of s_n?  CuriousKit  Math  15  20160131 11:57 
reserving a few k values  Trilo  Riesel Prime Search  7  20150927 23:20 
reserving a few k values  Trilo  Riesel Prime Search  0  20130825 14:47 
98.00M to 98.05M Excluded Values  storm5510  Lone Mersenne Hunters  45  20091113 19:35 