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Old 2003-06-06, 14:35   #1
ThomRuley's Avatar
May 2003

24810 Posts
Default 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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Old 2003-06-06, 14:41   #2
Axel Fox
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May 2003

1408 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.
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Old 2003-06-06, 15:17   #3
eepiccolo's Avatar
Dec 2002
Frederick County, MD

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You can find out a lot of information about trial factoring here:
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Old 2003-06-06, 19:33   #4
garo's Avatar
Aug 2002
Termonfeckin, IE

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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.
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Old 2003-06-07, 04:40   #5
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"Richard B. Woods"
Aug 2002
Wisconsin USA

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For a thorough earlier discussion, see the thread "Does the LL test:s factorization save or waste CPU time?" in The Software forum at, 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 (
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