Question on "ECM on Mersenne cofactor" work type

[mikedons]

I set Prime95 up to do the "ECM on Mersenne cofactor" work type and was sort of expecting that I would get an assignment that ran ECM on a cofactor of a Mersenne number many times, until it was deemed unproductive to continue. What actually happens is that I get an assignment to do ECM on a Mersenne number once, then it moves on to a different Mersenne number.

Using M2106347 as an example (approx 700000 decimal digits if my maths is correct), it has 4 known factors totalling about 50 decimal digits, so the remaining unfactored amount is relatively speaking a similar size to M2106347. Is this why we just repeat the ECM on M2106347 instead of on the unfactored amount?

I still don't understand the apparent scatter gun approach where I get assigned 1 attempt at many different exponents (rather than repeatedly trying to factor the same number).

[axn]

Originally Posted by mikedons

Using M2106347 as an example (approx 700000 decimal digits if my maths is correct), it has 4 known factors totalling about 50 decimal digits, so the remaining unfactored amount is relatively speaking a similar size to M2106347. Is this why we just repeat the ECM on M2106347 instead of on the unfactored amount?

It is more efficient to use the full mersenne number for the FFT operations (because of its special form) rather than just the unfactored part. In fact, even if the unfactored part was just half the size as the mersenne number, it would still be efficient to use the full number. However, rest assured, it will use the known factors while computing gcd so that only new factors will be reported. You're not losing anything.

Originally Posted by mikedons

I still don't understand the apparent scatter gun approach where I get assigned 1 attempt at many different exponents (rather than repeatedly trying to factor the same number).

Depth-first vs breadth-first search. Your best bet of finding a factor is to run ECM on the least ECM-ed number. Server will keep track.

[mikedons]

Thank you.

[piforbreakfast]

Originally Posted by axn

It is more efficient to use the full mersenne number for the FFT operations (because of its special form) rather than just the unfactored part. In fact, even if the unfactored part was just half the size as the mersenne number, it would still be efficient to use the full number. However, rest assured, it will use the known factors while computing gcd so that only new factors will be reported. You're not losing anything.



Depth-first vs breadth-first search. Your best bet of finding a factor is to run ECM on the least ECM-ed number. Server will keep track.

I've wondered for some time, what is the purpose in factoring numbers that have been found to be non-prime but which have not been fully factored?

[BudgieJane]

Originally Posted by piforbreakfast

I've wondered for some time, what is the purpose in factoring numbers that have been found to be non-prime but which have not been fully factored?

It's the same as climbing Everest, or other mountains that have been climbed before: "Because it's there."

[axn]

Originally Posted by piforbreakfast

I've wondered for some time, what is the purpose in factoring numbers that have been found to be non-prime but which have not been fully factored?

We get a shot at fully factoring them. They have some mathematical uses (or so I've been told), but is also a fun challenge. See https://www.mersenne.ca/prp.php for the current list of fully factored Mersenne numbers.

[mathwiz]

Originally Posted by piforbreakfast

I've wondered for some time, what is the purpose in factoring numbers that have been found to be non-prime but which have not been fully factored?

This is a good page with some answers to "why do we do X", where X could be prime hunting, factoring, etc. Ultimately it's your machine and your cycles, so you get to decide what seems most fun and rewarding to participate in.