mersenneforum.org What's the point of factoring known composites?
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 2011-02-20, 03:09 #1 ixfd64 Bemusing Prompter     "Danny" Dec 2002 California 2·11·107 Posts What's the point of factoring known composites? I've noticed that a lot of people are ECM'ing and P-1'ing Mersenne numbers that are known to be composite. Is there any reason for doing this? Generally, searching for small factors helps eliminates candidates for time-consuming primality tests. However, trying to factor composite numbers isn't going to help us find a new Mersenne prime. If we stopped assigning ECM factoring, we could reach those milestones a lot quicker. I know that many people like to find factors for the same reason we look for Mersenne primes: because they are there. However, there is no shortage of Mersenne factors, compared to, say, Fermat factors, which we know only a few hundred of. So my question is: what is the point of trying to factor numbers that are known to be composite, besides contributing to our mathematical knowledge?
 2011-02-20, 06:38 #2 Uncwilly 6809 > 6502     """"""""""""""""""" Aug 2003 101×103 Posts 9,209 Posts There numbers nerds want complete factorization of numbers. It helps them sleep at night. ECM and P-1 are better at that than TF.
 2011-02-20, 06:39 #3 Commaster   Jun 2010 Kiev, Ukraine 3·19 Posts As I understand, which is almost obviously not the actual reason, we are looking for more factors to run global filter jobs and eliminate a lot of candidates in one run. Please, tell me, there's more reason in doing it :)
2011-02-21, 10:37   #4

"Richard B. Woods"
Aug 2002
Wisconsin USA

22·3·641 Posts

Quote:
 Originally Posted by ixfd64 So my question is: what is the point of trying to factor numbers that are known to be composite, besides contributing to our mathematical knowledge?
Some of us want to do exactly the latter: contribute to mathematical knowledge.

2011-02-21, 11:51   #5
CRGreathouse

Aug 2006

3×1,987 Posts

Quote:
 Originally Posted by Commaster Please, tell me, there's more reason in doing it :)
Factors for small Mersenne numbers are extremely useful in producing lists of pseudoprimes, which in turn are used to make fast primality tests for small numbers.

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