Quote:
Originally Posted by R.D. Silverman
Kleinjung just found a p55 factor of M1079.
I am guessing that they might have been doing ECM pretesting
prior to doing GNFS on the number.

(topic: a previous miss?) This is c217, from c190c233, probably
difficulty above 250? The ones below 250 had 4t50, above 3t50.
We know that 4t50 tends to leave p53/p54's. I'm putting t55 at
c. 5.5t50; 2t55 at 11t50, so the previous test to 3t50 is perhaps
enough for a .33 chance of finding a known p55 (with t55 a .62 chance,
and 2t55 to "remove" p55's a .80 chance ... of finding a known p55).
Between Batalov+Dodson (below diff 250, mostly) and NFS@Home
(above 250, mostly) we're seeing a lot of numbers raised from
initial tests of 4t50, 3t50 and 2t50 (for c234c250) to 7t50  11t50
for sieving, and then actually getting the snfs factors to compare.
I'd consider Thorston's p55 to be fairly typical of what we expect
to find during the "ecm pretesting" (way too sparse for "ecm factoring").
Sam's page 112 and the current page 113 seem to be well representative
of how these have been turning out.
There's also a sprinkling of numbers that merit tests past 2t55
(a _very_ unrewarding range for ecm factoring). We have c180
gnfs and 11M583 sortof on the border, M941 and 5p398 and larger
gnfs in the range where we prefer _not_ to find p55p58's by
sieving. I'd agree that c217 gnfs is likely just off the horizon (for us).
In this range, the prize is still Aoki's p64 ecm factor of R311; after so
much effort towards the kilobit snfs that he's ambivalent about
whether to consider the p64 a success. Bruce