Responses to a couple of postings -- Steve Harris wrote: > 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,
"Better for the mathematical community as a whole" is actually almost exactly what I had in mind when I started composing that paragraph ... honest! But then I started revising, and lost some stuff in the process. Nevertheless, I stand by my assertion that "a 'Factored' status is better for GIMPS than a 'Two LL' status" ... insofar as our LL testing remains less reliable than our factor verification. Double-checking certainly improves LL result reliability, but I think our record shows that a verified factor is still slightly (by a minute but nonzero margin) more reliable an indicator of compositeness than two matching nonzero LL residues. (See earlier discussions of potential reasons for incorrect LL results. Some error sources would be more likely to affect the longer LL test than the shorter factor verification.) > It matters to those who are attempting to fully factor Mersenne > numbers, but that's a different project altogether, Some of us like to participate in both. :-) > 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. But if factoring is not really part of GIMPS's purpose (and I agree it isn't), how can a separate factoring effort be "behind" GIMPS at all? Aren't they measuring their progress in a different, non-comparable, dimension? > 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 :-) "A journey of a thousand miles begins with but a single step." Two million three-foot steps total more than one thousand miles. - - - - - In reply to a statement of mine about "the extra benefit of finding a specific factor", Daran G. wrote: >I can see no way of objectively quantifying this benefit. Well -- if there's no objective quantification of the extra benefit of finding a specific factor, then it seems to me that there's no objectively quantifiable justification for saying that it's not valuable to do a certain amount of "extra" P-1 factoring on a once-LL'd Mnumber. :) In response to my writing: >> 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. Daran G. wrote: >It seems to be implicitely acknowledged in the way the trial factoring >depths are determined. But don't forget that this refers to a depth determined by Prime95 _in the context of calculating the factoring tradeoff point for maximizing GIMPS throughput for the "Test=" worktype_, NOT the context of a "Factor=" or "Pminus1=" worktype where the user has explicitly specified factoring limits, possibly for reasons beyond the ken of Prime95. Daran continues: > 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. Yes. But that doesn't have to affect Prime95's calculation of tradeoff points _for maximizing throughput of the "Test=" worktype_. I'm not saying that Prime95 should incorporate into its calculations a nonzero value for the benefit of finding a specific factor. I'm saying that it is rational for someone to decide to factor past the Prime95-calculated tradeoff points, and that it is unjustified to criticize "extra" factoring on the grounds that going past the Prime95-calculated tradeoff points is wasted effort. Richard B. Woods _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
