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?

There numbers nerds want complete factorization of numbers. It helps them sleep at night. ECM and P-1 are better at that than TF.

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 :)

[QUOTE=ixfd64;253090]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?[/QUOTE]Some of us want to do exactly the latter: contribute to mathematical knowledge.

[QUOTE=Commaster;253102]Please, tell me, there's more reason in doing it :)[/QUOTE]

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.