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Old 2007-03-13, 13:58   #1
nuggetprime
 
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Default 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
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Old 2007-03-13, 14:26   #2
Kosmaj
 
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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.
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Old 2007-03-15, 03:09   #3
masser
 
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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,
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Old 2007-04-09, 11:27   #4
nuggetprime
 
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And how can I do an ecm on Riesel numbers?
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Old 2007-04-14, 09:16   #5
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Seems like nobody knows the answer...
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Old 2007-04-14, 22:25   #6
Kosmaj
 
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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
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