Quote:
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.
Quote:
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).

Depthfirst vs breadthfirst search. Your best bet of finding a factor is to run ECM on the least ECMed number. Server will keep track.