ECM sounds good to me. It needn't be George's ECM implementation, of
course. Paul Zimmermann's GMP-ECM runs a little more slowly on Mersenne
numbers, but it has the immense benefit of not being limited to Mersenne
numbers. I have been using it to factor Cullen and Woodall numbers, which
have the form n.2^n+1 and n.2^n-1 respectively. I'm sure there are still
quite a few factors left to be found which have under 30 digits, and so
should be discoverable with your machine. The reason for this optimism is
that my DECstations are about as fast as a 486-50, and they are finding
20-25 digit factors at the rate of about one a week each.
See http://www.loria.fr/~zimmerma/records/ecmnet.html for more details.
Paul
> -----Original Message-----
> From: Earle Goodman [mailto:[EMAIL PROTECTED]]
> Sent: Tuesday, September 15, 1998 5:48 AM
> To: Mersenne Mailing List
> Subject: Mersenne: Usefulness of 486-33
>
>
> I have an old computer that I am wondering what the best
> project is for it.
> I currently have it running ecm, but it takes about 4 hours
> per curve (for
> M(1871) with 250,000 bound). I was wondering if there was
> anything that I
> would be able to use it for that might be more fruitful? I have been
> thinking of switching it to doing something like Proth, but
> am unsure how
> useful it will be there... BTW, this machine is not connected to the
> internet so it would be something that I can set and run for
> a while... I
> would appreciate any comments.
>
> Earle (George) Goodman
> [EMAIL PROTECTED]
>
