Mersenne: Factoring Assignments: Are They Always "First-Time?"
Stefan Struiker writes: When a requested factoring assignment is listed with, say, 52 in an account log, does this mean it has been factored to 52 bits, but _without_ success? Yes, the number should have no factors less than 2^52. Or could a factor have already been found in some cases, but less than 52 bits long? Nope, unless the factor was not reported for some reason (bug, disk crash, etc.). My strategy in factoring 13.3 mill exponents and up, is to save L-L testing and DCing time by knocking some out early. Seem to be on a roll, too, with factors found 40% of the time, with a turnaround of 40 hours per. That's a very high rate of factors, I'd've thought, but that happens sometimes. In any case, Prime95 "knows" how much factoring work should be done for a particular Mersenne number before starting an LL test (first or double-check) on it and will do more factoring if the data it gets from Primenet (or other source) indicates the number has not been factored "enough". The predicated chances of finding a factor during trial and P-1 factoring is taken into account, along with how long the factoring takes to do and how long the two LL tests will take. So your phrase "knocking some out early" is exactly correct: if noone tries to factor a particular Mersenne number before it is given to a Prime95 that wants to run an LL test, that Prime95 will do some factoring first, usually before it even finishes the prior Mersenne number's LL test (to make sure it has "enough" work in worktodo.ini). Eric Hahn writes: If it's listed as 52 in the fact-bits column of the report, it means that it's been trial-factored thru 2^52 without any factors being found. Currently, all exponents thru Prime95's limit of 79.3M have been factored to at least 2^50... If a factor is found for an exponent, it's eliminated from further testing of any kind. Yup. Here's a short summary of my current data. For Mersenne numbers with prime exponent that have no LL test nor a factor, here are the smallest exponents trial factored only as far as the last column: M( 5178743 )U: 2^62 M( 8896813 )U: 2^61 M( 9993539 )U: 2^60 M( 10078559 )U: 2^55 M( 11300657 )U: 2^54 M( 11505331 )U: 2^53 M( 11521879 )U: 2^52 M( 20500019 )U: 2^51 M( 30100181 )U: 2^50 M( 79300037 )U: 2^45 M( 79306169 )U: 2^43 The exponents above 79.3 million have probably only been worked on by me, personally, since they're above Prime95's limit, but I'm still a bit surprised they haven't been factored further; trial factoring to the same depth is _easier_ for larger exponents, not harder. Jeff Woods writes: Isn't the factor itself verified? Yes, if only by me, as I noted in another thread in the last couple of weeks. Will http://www.garlic.com/~wedgingt/mersenne.html _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Factoring Assignments: Are They Always "First-Time?"
Jeff Woods wrote: >>being found. Currently, all exponents thru Prime95's limit of >>79.3M have been factored to at least 2^50... If a factor is >>found for an exponent, it's eliminated from further testing >>of any kind. > >Isn't the factor itself verified? Yes, it is. However, at least in the case of Prime95, George has written the code such that the factor is validated before it's even displayed as a being a factor and written to the results file. If it's invalid, the code continues as if the "factor" was never found... Eric _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Factoring Assignments: Are They Always "First-Time?"
>From: Jeff Woods <[EMAIL PROTECTED]> >To: [EMAIL PROTECTED] >Subject: Re: Mersenne: Factoring Assignments: Are They Always >"First-Time?" >Date: Sat, 17 Jun 2000 17:14:00 -0400 > >At 01:00 PM 6/17/00 -0700, you wrote: (snip) >>If a factor is >>found for an exponent, it's eliminated from further testing >>of any kind. > >Isn't the factor itself verified? I would assume it is, however verifying a factor takes well under a P-90 second. Nathan Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Factoring Assignments: Are They Always "First-Time?"
At 01:00 PM 6/17/00 -0700, you wrote: >being found. Currently, all exponents thru Prime95's limit of >79.3M have been factored to at least 2^50... If a factor is >found for an exponent, it's eliminated from further testing >of any kind. Isn't the factor itself verified? _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Factoring Assignments: Are They Always "First-Time?"
Stefan Struiker wrote: >When a requested factoring assignment is listed with, say, 52 in >an account log, does this mean it has been factored to 52 bits, >but _without_ success? Or could a factor have already been >found in some cases, but less than 52 bits long? If it's listed as 52 in the fact-bits column of the report, it means that it's been trial-factored thru 2^52 without any factors being found. Currently, all exponents thru Prime95's limit of 79.3M have been factored to at least 2^50... If a factor is found for an exponent, it's eliminated from further testing of any kind. Eric _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Factoring Assignments: Are They Always "First-Time?"
TeamG: When a requested factoring assignment is listed with, say, 52 in an account log, does this mean it has been factored to 52 bits, but _without_ success? Or could a factor have already been found in some cases, but less than 52 bits long? My strategy in factoring 13.3 mill exponents and up, is to save L-L testing and DCing time by knocking some out early. Seem to be on a roll, too, with factors found 40% of the time, with a turnaround of 40 hours per. Tell me I'm not just a Foole For Factores, "Donne, Anne Donne, Undone," Stefanovic _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
