Brian J Beesley writes:
Also this would catch those users still using 15.x, which doesn't
have the same automatic mechanism for intermediate check-ins.
It would also - improperly - catch those of us that can't use the
automatic networking but whose machines are slower than the estimate
for some reason. A participant without email access that sends me
USMail with his data now and then is about to get caught by this for
an exponent that he's working on; 60 days simply isn't going to be
enough even though the prediction was for less than 40 days.
I think trial factoring is far enough ahead that encouraging slow
machines to do that isn't going to be helpful. However, slow
machines can still run ECM factoring usefully. I think it would be
better to encourage them to try ECM.
Using slow machines for trial factoring still makes good sense to me;
if nothing else, it means the faster machines are spending that much
more time on LL tests, even if it is a small extra amount of time.
ECM, as you note, is also productive; small exponents should be
reserved with Paul Zimmerman of ECMNet (there's a link on
www.mersenne.org).
Also, P-1 factoring, using Factor98, is still useful, there are still
many exponents under 1000 that noone is working on, and it will work
on exponents thru 170,000. Reserve exponents for P-1 by sending me
email; I also have some Factor98 save files for many exponents.
(b) an annual prize for the numerically largest factor found during
each calendar year - though I don't know where the money would come
from.
Neither do I; I'm still kind of surprised someone is offering money
for the next Mersenne prime.
And it would have to be worded very carefully; I can give you lots of
very large factors quite quickly, including fifteen or more that are
almost certainly prime but noone has proven to be prime. The largest
is 9778 digits and would be the largest "hard" prime known by a wide
margin. Would any of them count? I can likely find almost
arbitrarily large ones in the future; how about them?
And a prize for the smallest new factor would be even easier to rig in
this fashion; I have a 10-15 year old program whose entire purpose is
to print out small factors of Mersennes in _factor_ order! See my old
postings about my "reverse method".
Will
