mersenneforum.org P-1 factoring
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 2007-03-13, 13:58 #1 nuggetprime     Mar 2007 Austria 2·151 Posts P-1 factoring How I can do P-1 factoring on candidates after sieving? I tried it with Prime95 but Prime95 said that all numbers don't need p-1 factoring? Can anyone help me out? nuggetprime
 2007-03-13, 14:26 #2 Kosmaj     Nov 2003 2·1,811 Posts Our exponents are too small for P-1 factoring and we are not doing it. Just plain sieving followed by LLR tests. I remember about 2 years ago Payam and the others searching for primes of form 5*2^n+1 and 7*2^n+1 did some tests and found that P-1 are too slow in comparison with primality tests (actually at the time they used PRP if I remember correctly). Their exponents were between 1.5 and 2M.
 2007-03-15, 03:09 #3 masser     Jul 2003 wear a mask 13·113 Posts To get mprime to perform P-1 factoring on k*b^n-1 with B1, B2; regardless of whether it's efficient or not, put the following in your worktodo.ini file: Pminus1=k,b,n,-1,B1,B2 ex: If you wanted to sieve 77*2^321098-1 with B1=11000 and B2 = 1100000, your worktodo.ini file would contain: Pminus1=77,2,321098,-1,11000,1100000 IIRC, a similar command works with prime95, with perhaps an additional ",0" at the end of the line. For base b = 2, I doubt this will be efficient for any n < 2 million. For some of my base b = 5 work, I've found that around n = 600,000, P-1 factoring becomes useful. Best regards, masser
 2007-04-09, 11:27 #4 nuggetprime     Mar 2007 Austria 4568 Posts And how can I do an ecm on Riesel numbers?
 2007-04-14, 09:16 #5 nuggetprime     Mar 2007 Austria 1001011102 Posts Seems like nobody knows the answer...
 2007-04-14, 22:25 #6 Kosmaj     Nov 2003 2×1,811 Posts Nugget, You can find details here. But as I told you it's not worth the trouble. We are already sieving to 10^12 (=1T) and in some cases to 10^13 (=10T), therefore ecm will have to be set to search for 17 or 18-digit factors. Parameters for 15 and 20 digit factors are given in the readme file, so you can try those to have an idea about exe times per curve. Then observe that at p15 at least 30 curves are required to find a factor with a reasonable probability (if it exists). That's why peoply run P-1 tests where a single curve may be enough, but only factors which satisfy certain conditions can be found. Last fiddled with by Kosmaj on 2007-04-14 at 22:26