Known factors report question

[petrw1]

For report: http://www.mersenne.org/report_factors/
At the bottom of the page is the note:

If a Mersenne number has been fully factored the largest factor is not listed.

but how do I know if a number has been fully factored?

If I take the Mersenne number and divide it by all the factors listed it can leave a very large remainder which may be very difficult for me to determine if it is prime or not.

[TimSorbet]

As partially discussed in this thread, the PrimeNet DB does not store whether the cofactor of Mersenne numbers is prime, PRP, composite, or unknown, but you can test it yourself with Prime95 with a line like 'PRP=1,2,1108369,-1,0,0,"24384119"'.
I, for one, think this (keeping track of the cofactors, possibly even allowing reservations and credit for work PRPing them) would be a good addition.
There is a thread somewhere that someone has recently been checking many Mersenne cofactors to see if they're PRP, but I can't recall where that is. You can also check the FactorDB, though that might not always have the best info on Mersenne cofactors for semi-large (e.g. p=~1M) numbers, and has a stated limit of ~ 200,000 digits.

[MatWur-S530113]

it is simply not to see at the factor status page if a number is fully factored or not. And the reason is, that a prp-test at the remainder cost nearly the same time as a LLT at the Mersenne-number. The server is not able to do this for every (small) factor, which is found by TF, p-1 or ecm...

You can run such a prp test for yourself with prime95.
1) stop prime95
2) add a line like:
PRP=1,2,1196473,-1,"973929023,9074489141119"
to worktodo.txt
3) restart prime95

this will run a prp-test at M1196473 with the known factor(s) 973929023 and 9074489141119

I already suggestet some months ago to do such a prp-test at least for M-numbers with exponent<=2^16+1 , but it has low priority at George's todo-list (because the main object of GIMPS is to find Mersenne-primes, not to find factors of Mersenne-composites. But the found factors prevent the project of running many unnecessary LLT's).

greetings
Matthias

[wblipp]

Originally Posted by petrw1

but how do I know if a number has been fully factored?

If I take the Mersenne number and divide it by all the factors listed it can leave a very large remainder which may be very difficult for me to determine if it is prime or not.

Will Edgington has a separate file for fully factored Mersenne numbers, and a special indicator in the regular files, too. As long as you are collecting the information from the internet anyway, you could expand your range.