Actually, Richard's statement that "a 'Factored' status is better for GIMPS than a 'Two LL' status" is not quite true. It's better for the mathematical community as a whole, but not for GIMPS. GIMPS is looking for primes, not factors, and without skipping over any. This means all candidates must be tested and the non-primes eliminated, and it doesn't matter whether they are eliminated by 'factored' or by 'two matching nonzero LL residues'. It matters to those who are attempting to fully factor Mersenne numbers, but that's a different project altogether, and one that is decades (at least) behind GIMPS. The only reason we do any factoring at all is to reduce the time spent on LL testing.
Besides, if you do manage to find a 75-digit factor of a 2-million-digit Mersenne number, that still leaves a 1999925-digit remainder. Really not much help :-) Regards, Steve Harris -----Original Message----- From: Daran <[EMAIL PROTECTED]> To: [EMAIL PROTECTED] <[EMAIL PROTECTED]> Date: Friday, November 30, 2001 2:00 AM Subject: Re: Factoring benefit/cost ratio (was: Mersenne: Fw: The Mersenne Newsletter, issue #18) >----- Original Message ----- >From: <[EMAIL PROTECTED]> >To: <[EMAIL PROTECTED]> >Sent: Saturday, November 24, 2001 6:49 PM >Subject: Factoring benefit/cost ratio (was: Mersenne: Fw: The Mersenne >Newsletter, issue #18) > >> But ones factoring benefit calculation might ["should" would be in >> line with the popular theme of prescribing what's best for other >> GIMPS participants :)] include not only the time savings of >> eliminating the need for one or two L-L tests, but also the extra >> benefit of finding a specific factor. > >I can see no way of objectively quantifying this benefit. > >> In the GIMPS Search Status table at www.mersenne.org/status.htm the >> march of progress is from "Status Unknown" to "Composite - One LL" to >> "Composite - Two LL" to ... "Composite - Factored". > >More desireable - whether or not recorded on that page - would be >"Composite - Least (or greatest) factor known". Most desireable (other than >"Prime") would be "Composite - Completely factored'. > >> This reflects the view (with which I agree) that it is more valuable >> to know a specific factor of a Mnumber than to know that a Mnumber is >> composite but not to know any specific factor of that Mnumber. >> >> So a "Factored" status is better for GIMPS than a "Two LL" status, but >> calculations of factoring benefit that consider only the savings of >> L-L test elimination are neglecting the difference between those two >> statuses. If one consciously wants to neglect that difference ... >> well, okay ... but I prefer to see that explicitly acknowledged. > >It seems to be implicitely acknowledged in the way the trial factoring >depths are determined. If one places a non-zero value on a known factor, >then the utility of extra factoring work on untested, once tested, and >verified composites would be increased. It would have to be set very high >indeed to make it worth while returning to verified composite Mersennes. > >> Richard Woods > >Daran G. > > >_________________________________________________________________________ >Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm >Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
