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Old 2014-06-05, 10:48   #1
tha
 
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Default 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?
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Old 2014-06-05, 11:59   #2
LaurV
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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
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Old 2014-06-05, 13:27   #3
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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
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Old 2014-06-05, 14:32   #4
tha
 
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Quote:
Originally Posted by tha View Post
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.
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Old 2014-06-05, 15:18   #5
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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.
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Old 2014-06-05, 15:23   #6
R.D. Silverman
 
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Quote:
Originally Posted by tha View Post
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.
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Old 2014-06-05, 15:30   #7
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One possible use might be prp testing the remaining cofactor
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Old 2014-06-05, 15:34   #8
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Quote:
Originally Posted by paulunderwood View Post
One possible use might be prp testing the remaining cofactor
And?
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Old 2014-06-05, 15:49   #9
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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
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Old 2014-06-05, 15:52   #10
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Quote:
Originally Posted by R.D. Silverman View Post
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.
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Old 2014-06-05, 16:43   #11
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Quote:
Originally Posted by paulunderwood View Post
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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