20031118, 06:22  #1  
Aug 2002
2^{3}×5^{2} Posts 
Missed small factors
k5gj, GP2, and I have been having a PM exchange about factors that were missed during trial factoring. This exchange was prompted by a message GP2 received from k5gj, who has been running P1 on exponents that have long since been verified composite by LL testing:
Quote:
Code:
Bit Report TF Exponent Depth Depth 1017111715779881 49.85 57 75649430225324231 56.07 59 95075864569432231 56.40 59 23522191782267041 54.38 59 I got pulled into this exchange because GP2 had recently run across a twoyear old posting of mine in a mailing list archive: Quote:


20031118, 06:23  #2 
Aug 2002
2^{3}·5^{2} Posts 
Date: Sun, 30 Sep 2001 15:26:51 0700
From: "Daniel Swanson" <email address deleted> Subject: Mersenne: Factoring failure? Yesterday I was assigned M7027303 to doublecheck. The number came with the claim that it had no factors less than 62 bits. But my P1 factorization of the number found this 55bit factor: [Sun Sep 30 13:53:26 2001] P1 found a factor in stage #1, B1=35000, B2=463750. UID: dswanson/nosnawsd, M7027303 has a factor: 31090234297428433 I thought this was mighty peculiar, so I stuck "Factor=7027303,0,0" into my worktodo file to force a complete refactorization of the number. Sure enough, about three minutes later out pops the result: [Sun Sep 30 15:06:10 2001] UID: dswanson/nosnawsd, M7027303 has a factor: 31090234297428433 Somebody wasted a lot of time doing a firsttime LL test on this number. Does anybody have any idea how common factoring errors might be in the "exponents not factored" database, particularly since doublechecks are not commonly done on the factoring results? Dan 
20031118, 06:24  #3 
Aug 2002
200_{10} Posts 
Date: Sun, 30 Sep 2001 16:07:34 0700
From: "Daniel Swanson" <email address deleted> Subject: Mersenne: Re: Factoring Failure? A followon to my previous message: I went through the Cleared Exponents report looking for other examples of factors found during doublechecks that should have been found during the initial factorization. I found the following 7 examples, including the one I just reported: 5977297 53 DF 6726544627832489 26Aug01 12:03 TempleUDI C031EBA9B 6019603 57 DF 137024179940485697 18Aug01 18:55 TempleUDI C031EBA9B 7019297 57 DF 160100125459121849 27Sep01 22:52 TempleUDI TD01489_Cub1 7020641 58 DF 226230108157229263 30Sep01 02:05 RayPelzer Homebase 7025987 56 DF 74052063365823791 30Sep01 01:12 shaneamy P600A 7027303 55 DF 31090234297428433 30Sep01 20:58 dswanson nosnawsd 10159613 56 DF 68279769831982367 19May01 10:13 hornup lbe_pc Seems to be a big clump in the 701xxxx  702xxxx range. Given that this is at the leading edge of numbers currently being assigned for doublechecks, I'd be willing to bet several more will turn up in the next few days. Were numbers in this range all originally factored by the same user or computer? Another interesting note: Given the number of different computers working doublechecks, what are the odds that TempleUDI/C031EBA9B would pick up TWO of these?!? Dan 
20031118, 06:25  #4 
Aug 2002
200_{10} Posts 
Date: Mon, 01 Oct 2001 15:01:05 0400
From: George Woltman <email address deleted> Subject: Re: Mersenne: Re: Factoring Failure? Hi, At 04:07 PM 9/30/2001 0700, Daniel Swanson wrote: >I went through the Cleared Exponents >report looking for other examples of factors found during doublechecks that >should have been found during the initial factorization. > 5977297 53 DF 6726544627832489 > 6019603 57 DF 137024179940485697 > 7019297 57 DF 160100125459121849 > 7020641 58 DF 226230108157229263 > 7025987 56 DF 74052063365823791 > 7027303 55 DF 31090234297428433 >10159613 56 DF 68279769831982367 >Were numbers in this range all originally factored by the same user or >computer? My logfiles from that long ago have been zipped and stored on CDROM. It is possible that 7,010,000  7,030,000 were all factored by one person. It was not uncommon for me to hand out large blocks for factoring to users without Internet connections. While I no longer do this, there are a handful of users prefactoring the 20,000,000  80,000,000 area. I hope their machines are reliable!! They probably are as they are finding the expected number of factors. Anyway, it doesn't appear to be a program bug as you were able to find the factor with trial factoring. I'm guessing either bad hardware or an older prime95 version had a bug. Either way, GIMPS has never considered missing a factor as a big deal. It only means some wasted effort running a LL test that could have been avoided. Thanks for the interesting findings! Regards, George 
20031118, 06:26  #5 
Aug 2002
2^{3}×5^{2} Posts 
Date: Mon, 1 Oct 2001 22:23:38 +0200
From: "JeanYves Canart" <email address deleted> Subject: FW: Mersenne: Re: Factoring Failure? Hello all, I have browsed some logs I archived long time ago and I have found this: In may 1998, one user, "tomfakes", cleared around 80 exponents with factor found = "1" It was in the range 70130007055000. Regards, JeanYves 
20031118, 06:26  #6 
Aug 2002
2^{3}·5^{2} Posts 
Date: Tue, 2 Oct 2001 19:52:42 0000
From: bjb <email address deleted> Subject: Re: FW: Mersenne: Re: Factoring Failure? On 1 Oct 2001, at 22:23, JeanYves Canart wrote: > I have browsed some logs I archived long time ago and I have found > this: > > In may 1998, one user, "tomfakes", cleared around 80 exponents with > factor found = "1" It was in the range 70130007055000. Well, (s)he's not lying  0 = n (mod 1) is a property of integers ;) In any event: (a) this is the _opposite_ of the reported problem  what seems to have happened is that "no factor found" was being reported, sometimes erroneously; (b) this won't get through now PrimeNet validates submitted factors; the code I wrote for this purpose rejects as garbage any singledigit factor, after stripping off any leading zeroes as well as white space. (Obviously a Mersenne number with a prime exponent p > 5 cannot have any factors less than 10, and we know pretty much all there is to know about exponents up to and including 5, so excluding these is not a practical problem). > > At 04:07 PM 9/30/2001 0700, Daniel Swanson wrote: > > >I went through the Cleared Exponents > > >report looking for other examples of factors found during > > doublechecks that > > >should have been found during the initial factorization. > > > 5977297 53 DF 6726544627832489 > > > 6019603 57 DF 137024179940485697 > > > 7019297 57 DF 160100125459121849 > > > 7020641 58 DF 226230108157229263 > > > 7025987 56 DF 74052063365823791 > > > 7027303 55 DF 31090234297428433 > > >10159613 56 DF 68279769831982367 > > >Were numbers in this range all originally factored by the same user > > >or computer? > > > > My logfiles from that long ago have been zipped and stored on CDROM. > > It is possible that 7,010,000  7,030,000 were all factored by one > > person. It was not uncommon for me to hand out large blocks for > > factoring to users without Internet connections. While I no longer > > do this, there are a handful of users prefactoring the 20,000,000  > > 80,000,000 area. I hope their machines are reliable!! They > > probably are as they are finding the expected number of factors. The primes from that block of 20,000 numbers represents quite a bit of work and maps poorly onto the "missed" factors reported. A few mistakes are inevitable but, since testing a factor takes of the order of a microsecond on current systems, hardware glitches shouldn't be much of a risk. (? Unless they get into the code stream used to generate potential factors?) Reports of two "missed" factors of exponents within spitting distance of 6,000,000 and no less than four just over 7,000,000 looks high for random glitches to be responsible, even on really ropy hardware. Remember that P1 (which found the factors missed by trial factoring) can only find a small proportion of the "small" factors, especially when it's being run with "double checking" limits. > > > > Anyway, it doesn't appear to be a program bug as you were able to > > find the factor with trial factoring. I'm guessing either bad > > hardware or an older prime95 version had a bug. If it _was_ Prime95. There are other factoring programs out there; maybe there was a higher incidence of use about 3.5 years ago when these exponents would have been the subject of factoring assignments. > > Either way, GIMPS > > has never considered missing a factor as a big deal. It only means > > some wasted effort running a LL test that could have been avoided. True enough  though I'm concerned that the "no factors below 2^N" database may be seriously flawed, from the point of view of GIMPS it would seem to be a waste of time to go round redoing trial factoring just to fix this problem. However if it could be established that all the "missed" factors reported were the work of one user, perhaps it would be worth fixing the database to force rerunning of trial factoring for those factoring assignments run by that user when the exponents are reassigned for double checking (or LL testing). Regards Brian Beesley 
20031118, 06:27  #7 
Aug 2002
C8_{16} Posts 
Date: Tue, 2 Oct 2001 23:09:31 0500
From: "Steve Harris" <email address deleted> Subject: Re: FW: Mersenne: Re: Factoring Failure? > > Either way, GIMPS > > has never considered missing a factor as a big deal. It only means > > some wasted effort running a LL test that could have been avoided. >True enough  though I'm concerned that the "no factors below 2^N" >database may be seriously flawed, from the point of view of GIMPS >it would seem to be a waste of time to go round redoing trial >factoring just to fix this problem. Yes, from the point of view of GIMPS (that is, searching for Mersenne primes) it's not a huge deal... but there also exists an effort to fully factor the candidates that are not prime, and this throws a big problem into that project. Someone could be trial factoring an exponent from 2^59 to 2^65 and find a factor in that range after a smaller factor had been missed, and it will go into the database as the smallest factor when it actually is not. Might be decades before the smaller factor is discovered. Oh well, Steve 
20031118, 06:28  #8 
Aug 2002
200_{10} Posts 
Date: Wed, 3 Oct 2001 02:30:10 0400
From: "Carleton Garrison" <email address deleted> Subject: Re: FW: Mersenne: Re: Factoring Failure? > At 04:07 PM 9/30/2001 0700, Daniel Swanson wrote: > >I went through the Cleared Exponents > >report looking for other examples of factors found during > doublechecks that > >should have been found during the initial factorization. > > 5977297 53 DF 6726544627832489 > > 6019603 57 DF 137024179940485697 > > 7019297 57 DF 160100125459121849 > > 7020641 58 DF 226230108157229263 > > 7025987 56 DF 74052063365823791 > > 7027303 55 DF 31090234297428433 > >10159613 56 DF 68279769831982367 > >Were numbers in this range all originally factored by the same user > >or computer? > Either way, GIMPS > has never considered missing a factor as a big deal. It only means > some wasted effort running a LL test that could have been avoided. I wonder if by using configuration settings, people are able to skip as many, if not all, factoring stages? I believe the idea of trying to skip P1 factoring was talked about within the last 3 or 4 months. Apparently there are people who would just prefer to get credit for doing LL work than to find factors. Until factoring time (while one is LL testing) is at credited at the same same rate as LL testing, let alone getting credited not at all (most of the time no factors are found), results like the above could become common place. 
20031118, 06:28  #9 
Aug 2002
11001000_{2} Posts 
Date: Wed, 3 Oct 2001 02:41:27 0500 (CDT)
From: ribwoods <email address deleted> Subject: Mersenne: Re: Factoring Failure? Daniel Swanson wrote: > 5977297 53 DF 6726544627832489 > 6019603 57 DF 137024179940485697 > 7019297 57 DF 160100125459121849 > 7020641 58 DF 226230108157229263 > 7025987 56 DF 74052063365823791 > 7027303 55 DF 31090234297428433 >10159613 56 DF 68279769831982367 I'm pretty sure the second column is the previous trialfactoring limit, in units of powerof2. For M7019297, the found factor 160100125459121849 is larger than 2^57 (= 144115188075855872), and for M7025987, factor 74052063365823791 is greater than 2^56 (= 72057594037927936). Unless I'm misinterpreting something, those two cases don't indicate a trialfactoring failure. [dswanson comment on this posting: ribwoods is correct about the bit depth of the found factor. For example, the bit depth of 160100125459121849 is 57.15, which rounds down to the "57" listed. But ribwoods missed the point, which is that nofactor.txt had claimed that this exponent had no factor below 2^62. So it is indeed a trialfactoring failure.] 
20031118, 06:29  #10 
Aug 2002
2^{3}×5^{2} Posts 
Date: Wed, 3 Oct 2001 12:40:29 0400
From: "Carleton Garrison" <email address deleted> Subject: Re: FW: Mersenne: Re: Factoring Failure? > > I believe the idea of trying to skip P1 factoring was talked about within > > the last 3 or 4 months. Apparently there are people who would just prefer > > to get credit for doing LL work than to find factors. > > This is why I like that you loose credit for a LLtest if someone else > finds a factor later, or if two other independant checks prove your > result to be wrong. Me too. I understand that George's top producer page does this, while the PrimeNet stat page does not. PrimeNet really needs this capability. Carleton Garrison LL#163 F#295 G#253 www.teamprimerib.com 
20031118, 06:30  #11 
Aug 2002
200_{10} Posts 
Date: Wed, 03 Oct 2001 18:29:52 0700
From: Gerry Snyder <email address deleted> Subject: Re: FW: Mersenne: Re: Factoring Failure? Carleton Garrison wrote: > > [? wrote:] > > > > This is why I like that you lose credit for a LLtest if someone else > > finds a factor later, or if two other independant checks prove your > > result to be wrong. > > Me too. I understand that George's top producer page does this, while the > PrimeNet stat page does not. PrimeNet really needs this capability. To me, there is no question that an LL test that is shown to be wrong should not count for anything. The number still required two more LL tests, so that it as if the erroneous one had not been done. But, at least in theory, every Mersenne number proven nonprime will eventually be factored. Again, to me, so what? At least the LL test showed that further factoring activity would eventually succeed. I have nothing against George doing things that way. (When I play ball with him, I play by his rules or I don't play at all. You know why? Because it's his ball, that's why.) Seriously, I can see some point to doing things that way, but I would do probably do it differently. But even more seriously, I'm just glad to be in the game, and I am grateful to George and all the others who have made it easy and fun to participate. Gerry PS I just got a chuckle from imagining a very competitive team tearing down an opponent by finding what numbers the opponent had done LL tests on, and factoring them. 
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