20070313, 13:58  #1 
Mar 2007
Austria
2·151 Posts 
P1 factoring
How I can do P1 factoring on candidates after sieving? I tried it with Prime95 but Prime95 said that all numbers don't need p1 factoring?
Can anyone help me out? nuggetprime 
20070313, 14:26  #2 
Nov 2003
2·1,811 Posts 
Our exponents are too small for P1 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 P1 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. 
20070315, 03:09  #3 
Jul 2003
wear a mask
13·113 Posts 
To get mprime to perform P1 factoring on k*b^n1 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*2^3210981 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, P1 factoring becomes useful. Best regards, masser 
20070409, 11:27  #4 
Mar 2007
Austria
456_{8} Posts 
And how can I do an ecm on Riesel numbers?

20070414, 09:16  #5 
Mar 2007
Austria
100101110_{2} Posts 
Seems like nobody knows the answer...

20070414, 22:25  #6 
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 18digit 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 P1 tests where a single curve may be enough, but only factors which satisfy certain conditions can be found. Last fiddled with by Kosmaj on 20070414 at 22:26 