trial factoring of "small" mersenne numbers

antiroach · 2003-07-15, 01:54

i noticed that there are many "small" mersenne numbers that have only been trial divided upto 57 bits. (decomp -w 1 100000) for example. I tried to trial factor them (upto 58 bits) just for the heck of it but prime95 wouldnt let me. It said it was a bad factoring assignment. Anyone know why this is happening? Thanks.

NickGlover · 2003-07-15, 05:00

I believe you need to set FactorOverride=58 in prime.ini .

The reason you get "bad factoring assignment" is that default factoring depth for an exponent around 1 million is much lower than 57 bits, so Prime95 doesn't think there is any work to do on the exponent.

cheesehead · 2003-07-15, 05:40

Quote:

Originally Posted by antiroach

i noticed that there are many "small" mersenne numbers that have only been trial divided upto 57 bits. (decomp -w 1 100000) for example. I tried to trial factor them (upto 58 bits) just for the heck of it

I hope you're aware that trial-factoring a small Mnumber from 2^57 to 2^58 takes _longer_ than TFing a large Mnumber from 2^57 to 2^58, and that the ratio is roughly the inverse of the ratio of exponents. That is, it takes in the neighborhood of 100 times as long to TF 2^9xxxx-1 from 2^57 to 2^58 as it does to TF 2^9xxxxxx-1 from 2^57 to 2^58. That ratio is offset by a mildly faster TF iteration speed for the smaller Mnumber, but that offset is of a lower order than the exponent ratio.

eepiccolo · 2003-07-15, 11:50

Also, reference this post for another reason you shouldn't TF the smaller numbers.

http://www.mersenneforum.org/viewtopic.php?t=415

antiroach · 2003-07-15, 16:56

wow, thanks for all the replies. i did set factoroverride, but i had no idea that it takes longer to trial factor smaller numbers. I wasn't really planning on trial factoring those numbers since an first time LL and a double check were already performed on these numbers. I was just wondering why prime95 wouldn't even let me do it.

NickGlover · 2003-07-15, 17:50

I just tested to make sure and it does work. I randomly chose 944821 from the nofactor file. My worktodo.ini has Factor=944821,57 and I set FactorOverride=58 in prime.ini . Make certain to restart Prime95 after making changes to prime.ini .

antiroach · 2003-07-16, 23:35

i have only tested it upto 100,000. I havent bothered trying to trial factor anything above that. :)

2003-07-15, 01:54	#1
antiroach Jun 2003 2²·61 Posts	trial factoring of "small" mersenne numbers i noticed that there are many "small" mersenne numbers that have only been trial divided upto 57 bits. (decomp -w 1 100000) for example. I tried to trial factor them (upto 58 bits) just for the heck of it but prime95 wouldnt let me. It said it was a bad factoring assignment. Anyone know why this is happening? Thanks.

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2003-07-15, 05:00	#2
NickGlover Aug 2002 Richland, WA 84₁₆ Posts	I believe you need to set FactorOverride=58 in prime.ini . The reason you get "bad factoring assignment" is that default factoring depth for an exponent around 1 million is much lower than 57 bits, so Prime95 doesn't think there is any work to do on the exponent.

2003-07-15, 11:50	#4
eepiccolo Dec 2002 Frederick County, MD 2·5·37 Posts	Also, reference this post for another reason you shouldn't TF the smaller numbers. http://www.mersenneforum.org/viewtopic.php?t=415

2003-07-15, 16:56	#5
antiroach Jun 2003 F4₁₆ Posts	wow, thanks for all the replies. i did set factoroverride, but i had no idea that it takes longer to trial factor smaller numbers. I wasn't really planning on trial factoring those numbers since an first time LL and a double check were already performed on these numbers. I was just wondering why prime95 wouldn't even let me do it.

2003-07-15, 17:50	#6
NickGlover Aug 2002 Richland, WA 2²·3·11 Posts	I just tested to make sure and it does work. I randomly chose 944821 from the nofactor file. My worktodo.ini has Factor=944821,57 and I set FactorOverride=58 in prime.ini . Make certain to restart Prime95 after making changes to prime.ini .

2003-07-16, 23:35	#7
antiroach Jun 2003 2²·61 Posts	i have only tested it upto 100,000. I havent bothered trying to trial factor anything above that. :)