On 1 Nov 00, at 18:17, David A. Miller wrote:
> The last machine that I had working on M727 has finished its 1000 curves
> at B1=44M. This is enough to finish the recommended number of curves at
> that bound. Thus there are probably no factors below 10^50, and it won't
> be practical to find the factors with ECM.
The question arises as to whether or not it is economical to continue
beyond B1=44000000, B2=4290000000. This may be a function of the
native integer size - 64-bit systems shouldn't have any problems
(given a suitable implementation)
I guess the special number field people will take an interest as soon
as they've cleared whatever they're working on at the moment.
>
> Have any other numbers received as much ECM effort as this? I'm betting
> that there aren't many.
Possibly not - even if the curves for B1=44000000 B2=4290000000 have
been done, they've probably been done on a smaller exponent,
therefore with less expenditure of time.
Although the curves completed don't look as good, it is, however,
possible that more CPU time has been expended trying to factor some
of the Fermat numbers using ECM.
There's still plenty of work for you to do!
Regards
Brian Beesley
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