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 2014-06-05, 10:48 #1 tha     Dec 2002 36016 Posts option for finding multiple factors during trial factoring I tried undoc, readme and google but couldn't find the information I was looking for. If I got it right mprime (or prime95) stops looking for more factors when it has found a factor during trial factoring, so the line Factor=N/A,some_exponent,0,56 returns 1 factor at most. Again, if I am correct. Is there an option to force it to find all factors between 0 and 56 bits using only trial factoring?
 2014-06-05, 11:59 #2 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 101000001000102 Posts No. For GIMPS (i.e. finding primes) the exponent falls from grace once a factor is found (i.e. is composite). And you should not use P95 anymore for doing TF. This because GPUs do TF from 100 to 300 times faster. Even if you have an antediluvian CPU/system which could not run P-1 or DC (i.e. slow, no memory), keeping it running for just TF is not justified economically [edit: better load yafu and work some aliquots on it]. You could get a low-range GPU and do the same TF work in less time and with lower electricity bill. My two cents. Everybody is free to do whatever work he wants with his resources. Last fiddled with by LaurV on 2014-06-05 at 12:00
 2014-06-05, 13:27 #3 Stargate38     "Daniel Jackson" May 2011 14285714285714285714 3×251 Posts If you want to do more than 1 factor, use factor5. That doesn't stop at the 1st factor. (Google it if you need to) Last fiddled with by Stargate38 on 2014-06-05 at 13:28 Reason: fix smilie
2014-06-05, 14:32   #4
tha

Dec 2002

25×33 Posts

Quote:
 Originally Posted by tha Again, if I am correct. Is there an option to force it to find all factors between 0 and 56 bits using only trial factoring?
Hmm, the data is in and prime95 does return all factors between both limits. Problem solved.

 2014-06-05, 15:18 #5 kracker     "Mr. Meeseeks" Jan 2012 California, USA 27×17 Posts Yes... it's really not worth TF'ing on the CPU at all in my opinion... especially with factor5. I think it was mainly made/optimized for the very high ranges (Operation Billion Digits) For example: TF'ing a 55M number from 58 to 59 bits takes 51 seconds on a haswell core.
2014-06-05, 15:23   #6
R.D. Silverman

"Bob Silverman"
Nov 2003
North of Boston

22·1,877 Posts

Quote:
 Originally Posted by tha I tried undoc, readme and google but couldn't find the information I was looking for. If I got it right mprime (or prime95) stops looking for more factors when it has found a factor during trial factoring, so the line Factor=N/A,some_exponent,0,56 returns 1 factor at most. Again, if I am correct. Is there an option to force it to find all factors between 0 and 56 bits using only trial factoring?
What purpose is served by finding more than one factor?

GIMPS is looking for Mersenne Primes. The purpose of TF is to quickly
eliminate candidates that have small prime factors so that they need
not run a full LL test. Once a factor is found, we know the number is
composite.

Move on.

 2014-06-05, 15:30 #7 paulunderwood     Sep 2002 Database er0rr 7·641 Posts One possible use might be prp testing the remaining cofactor
2014-06-05, 15:34   #8
R.D. Silverman

"Bob Silverman"
Nov 2003
North of Boston

1D5416 Posts

Quote:
 Originally Posted by paulunderwood One possible use might be prp testing the remaining cofactor
And?

 2014-06-05, 15:49 #9 paulunderwood     Sep 2002 Database er0rr 7·641 Posts Maybe to top this The Prime Pages table for Mersenne cofactors However, if it is beyond proof, then it might be added to Henri Lifchitz's PRP database. Last fiddled with by paulunderwood on 2014-06-05 at 16:01
2014-06-05, 15:52   #10
science_man_88

"Forget I exist"
Jul 2009
Dartmouth NS

2·3·23·61 Posts

Quote:
 Originally Posted by R.D. Silverman What purpose is served by finding more than one factor?
I could see eliminating possible candidates for other prime exponents if the factor is still small enough to be useful, for example 7,21,35,49,... all divide by 7
and are 1 mod :

Code:
(12:44) gp > forstep(x=1,100,2,a=7*x;print(factor(a-1)))
[2, 1; 3, 1]
[2, 2; 5, 1]
[2, 1; 17, 1]
[2, 4; 3, 1]
[2, 1; 31, 1]
[2, 2; 19, 1]
[2, 1; 3, 2; 5, 1]
[2, 3; 13, 1]
[2, 1; 59, 1]
[2, 2; 3, 1; 11, 1]
[2, 1; 73, 1]
[2, 5; 5, 1]
[2, 1; 3, 1; 29, 1]
[2, 2; 47, 1]
[2, 1; 101, 1]
[2, 3; 3, 3]
[2, 1; 5, 1; 23, 1]
[2, 2; 61, 1]
[2, 1; 3, 1; 43, 1]
[2, 4; 17, 1]
[2, 1; 11, 1; 13, 1]
[2, 2; 3, 1; 5, 2]
[2, 1; 157, 1]
[2, 3; 41, 1]
[2, 1; 3, 2; 19, 1]
[2, 2; 89, 1]
[2, 1; 5, 1; 37, 1]
[2, 7; 3, 1]
[2, 1; 199, 1]
[2, 2; 103, 1]
[2, 1; 3, 1; 71, 1]
[2, 3; 5, 1; 11, 1]
[2, 1; 227, 1]
[2, 2; 3, 2; 13, 1]
[2, 1; 241, 1]
[2, 4; 31, 1]
[2, 1; 3, 1; 5, 1; 17, 1]
[2, 2; 131, 1]
[2, 1; 269, 1]
[2, 3; 3, 1; 23, 1]
[2, 1; 283, 1]
[2, 2; 5, 1; 29, 1]
[2, 1; 3, 3; 11, 1]
[2, 5; 19, 1]
[2, 1; 311, 1]
[2, 2; 3, 1; 53, 1]
[2, 1; 5, 2; 13, 1]
[2, 3; 83, 1]
[2, 1; 3, 1; 113, 1]
[2, 2; 173, 1]
respectively so for example we know 35 isn't prime but that eliminates k=1 for p=17. the lower the factor the better though since it eliminates 1/factor k in theory if it divides one.

2014-06-05, 16:43   #11
R.D. Silverman

"Bob Silverman"
Nov 2003
North of Boston

750810 Posts

Quote:
 Originally Posted by paulunderwood Maybe to top this The Prime Pages table for Mersenne cofactors However, if it is beyond proof, then it might be added to Henri Lifchitz's PRP database.
Golllleee!

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