Yvan Dutil writes:
Maybe a multi-level objective would be better. Say for 2001:
-Exploration factoring up to 15 000 000
Depending on what you mean by "exploration", this is already done thru
21.5 million or so.
-one L-L up to 10 000 000
-two L-L up to 6 000 000
Others can almost certainly better estimate how likely these are.
-ECM complete factoring up to 100 000
This is, I think, wildly optimistic; it's quite likely that there will
still be Mersenne numbers with exponents under 1000 that are not
completely factored by 2001. M727 still has no known factors, for
example, and no ECM effort for any exponent above 23,059 has been
reported to me; in contrast, there's been some P-1 effort to just
under 170,000. Further, there are far fewer people running ECM (or
P-1) factoring than there are people running Lucas-Lehmer tests and
'complete' factoring is much harder than LL tests for the same
exponent.
There are still exponents under 1000 that noone is running P-1 on,
for that matter; if you want to reserve some, send me email.
Will
