mersenneforum.org What's the point of factoring known composites?
 Register FAQ Search Today's Posts Mark Forums Read

 2011-02-20, 03:09 #1 ixfd64 Bemusing Prompter     "Danny" Dec 2002 California 2×29×43 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 10,891 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

11110000011002 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

5,987 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.

 2022-12-03, 07:45 #6 ixfd64 Bemusing Prompter     "Danny" Dec 2002 California 1001101111102 Posts I'm aware this is a very old thread, but I suddenly realized there is another good reason to factor composite Mersenne numbers: every factor found is a potential counterexample to the conjecture that all Mersenne numbers are square-free.
2022-12-06, 22:29   #7
GP2

Sep 2003

3×863 Posts

Quote:
 Originally Posted by ixfd64 every factor found is a potential counterexample to the conjecture that all Mersenne numbers are square-free.
And of course, finding a non-square-free Mersenne numbers would mean finding a Wieferich prime.

https://primes.utm.edu/notes/proofs/SquareMerDiv.html

 Similar Threads Thread Thread Starter Forum Replies Last Post gd_barnes Conjectures 'R Us 57 2011-09-12 12:31 Thomas11 Riesel Prime Search 32 2008-11-20 21:04 AntonVrba Factoring 3 2006-02-05 06:30 mfgoode Miscellaneous Math 12 2005-07-05 19:19 dsouza123 Software 3 2003-09-21 12:46

All times are UTC. The time now is 14:05.

Mon Jan 30 14:05:25 UTC 2023 up 165 days, 11:33, 0 users, load averages: 2.36, 2.15, 1.99