Trial-factoring efficiency

ThomRuley · 2003-06-06, 14:35

I have a question for those of you who have more experience with factoring ranges. I was wondering what percentage of exponents I can expect to eliminate by trial-factoring to 60 bits. And for those of you who are factoring past 60 bits, what percentage does each extra bit eliminate?

Axel Fox · 2003-06-06, 14:41

Well, I don't have a lot of experience yet, but I know it depends strongly on how far the range has already been factored.

In my range, it was factored to 58 bits and I'm factoring to 60 bits and I get about 90 factors found per range of 100.000 (from 30.000.000 to 30.100.000 for example).

Axel Fox.

eepiccolo · 2003-06-06, 15:17

You can find out a lot of information about trial factoring here: http://www.mersenne.org/math.htm.

garo · 2003-06-06, 19:33

A simple rule is that factoring for n bits removes 1/n factors. So if you factor from 58 to 60 bits (2 bits only) you will find a factor every 2/60 = 1/30 exponents.

cheesehead · 2003-06-07, 04:40

For a thorough earlier discussion, see the thread "Does the LL test:s factorization save or waste CPU time?" in The Software forum at http://www.mersenneforum.org/viewtopic.php?t=78, especially svempasnake's table comparing the 1/n prediction to the actual number of factors found, on page 3 at Mon Sep 16, 2002 9:32 pm (http://www.mersenneforum.org/viewtop...highlight=#895).

2003-06-06, 14:35	#1
ThomRuley May 2003 294₁₀ Posts	Trial-factoring efficiency I have a question for those of you who have more experience with factoring ranges. I was wondering what percentage of exponents I can expect to eliminate by trial-factoring to 60 bits. And for those of you who are factoring past 60 bits, what percentage does each extra bit eliminate?

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2003-06-06, 14:41	#2
Axel Fox May 2003 2⁵×3 Posts	Well, I don't have a lot of experience yet, but I know it depends strongly on how far the range has already been factored. In my range, it was factored to 58 bits and I'm factoring to 60 bits and I get about 90 factors found per range of 100.000 (from 30.000.000 to 30.100.000 for example). Axel Fox.

2003-06-06, 15:17	#3
eepiccolo Dec 2002 Frederick County, MD 370₁₀ Posts	You can find out a lot of information about trial factoring here: http://www.mersenne.org/math.htm.

2003-06-06, 19:33	#4
garo Aug 2002 Termonfeckin, IE 2⁴×173 Posts	A simple rule is that factoring for n bits removes 1/n factors. So if you factor from 58 to 60 bits (2 bits only) you will find a factor every 2/60 = 1/30 exponents.

2003-06-07, 04:40	#5
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 1E0C₁₆ Posts	For a thorough earlier discussion, see the thread "Does the LL test:s factorization save or waste CPU time?" in The Software forum at http://www.mersenneforum.org/viewtopic.php?t=78, especially svempasnake's table comparing the 1/n prediction to the actual number of factors found, on page 3 at Mon Sep 16, 2002 9:32 pm (http://www.mersenneforum.org/viewtop...highlight=#895).