Mersenne: New exponents
Hi from Ireland - I have a few questions about how M39 will affect the allocation of current/new exponents. Once the result has been announced I suppose we will recommence searching above M39? I got a couple of new exponents over the weekend - I assume that they are not necessarily M39 in order to maintain secrecy. If so then, after the announcement, should we dump our existing tests or finish off factoring things that are half finished? Does prime95 handle this scenario automatically - i.e. will new exponents be automatically sent if a manual update is done? Thanks, Keith The information in this email is confidential and may be legally privileged. It is intended solely for the addressee. Access to this email by anyone else is unauthorized. If you are not the intended recipient, any disclosure, copying, distribution or any action taken or omitted to be taken in reliance on it, is prohibited and may be unlawful. When addressed to our clients any opinions or advice contained in this email are subject to the terms and conditions expressed in the governing Ark Life agreement. This communication represents the originators personal views and opinions which do not necessarily reflect those of Ark Life. If you receive this email in error, please immediately notify Ark Life's Networking team at +353 (0)1 6681199. _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: Re: Factoring benefit/cost ratio
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]] (Aside - we're rather more likely to find a 75-bit factor than a 75- digit factor. In fact, finding a 75-digit prime factor of a no factors known Mersenne number with an exponent under 80 million would be a significant achievement in itself. Finding a 75-digit prime and non-algebraic factor of any integer with more than, say, 200 digits would be a significant achievement. The record today is 55 digits; it reached 53 digits 3 years ago and only a handful of factors with 50 or more digits have been found ever. I have precisely one of them to my credit 8-) At the moment, having found one factor, we quit. That's sufficient effort for the purpose of trying to find Mersenne primes. A little more work might break the cofactor down further. Actually, some of us don't quit. But we're a small bunch of weirdos, and we only work on tiny exponents anyway. Paul _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: New exponents
Hi Keith, At 02:53 PM 12/3/2001 +, Keith Garland wrote: Hi from Ireland - I have a few questions about how M39 will affect the allocation of current/new exponents. Once the result has been announced I suppose we will recommence searching above M39? The GIMPS project is dedicated to finding ALL Mersenne primes within reach of today's computers. The server will continue to hand out the smallest available exponents without regard for M39. If you find a new prime smaller than M39, you have found something *really* rare - an out-of-order Mersenne prime. Only one of those as ever been found when Welsh and Colquitt found M110503. Some argue that M4253 was found out-of-order, but the computer discovered it in-order Most new assignments will be above M39 anyway, but if you only want world-record candidates and the server sends you a small one then send me an email and I'll email you a bigger one to test. I'll also add your suggestion to the program's wish list. Best regards, George _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: New exponents
At 10:19 AM 12/4/2001 -0500, George Woltman wrote: If you find a new prime smaller than M39, you have found something *really* rare - an out-of-order Mersenne prime. Only one of those as ever been found when Welsh and Colquitt found M110503. Some argue that M4253 was found out-of-order, but the computer discovered it in-order For the information of the list, the folks who *want* to try to get exponents below (the presumed) M#39 might want to look into manually fetching work at 2:00 (IIRC) in the morning Eastern standard (7 or 8 GMT), when the server releases exponents of folks who have stopped participating without properly quitting. You face a small risk that the original tester will submit a result, but even in that case you'll get credit for the double-check (though that would be a small consolation if a prime were found). Nathan _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: SF Bay area GIMPS party
1) Tied House, Mountain View 2) Faultline Brewery, Sunnyvale either, orther, as far as I care... heh. re: ride sharing, I have a new 7 passenger van, and might be able to carpool folks from the Santa Cruz area... assuming I can go (I've got to check with SWMBO to make sure we don't have a prior engagement on that date). SWMBO says 'sure'. So... anyone in the Santa Cruz area wants a ride up and back, let me know by friday. I could haul as many as 6 extra folks in reasonable comfort (I gotta brand new Ford E150 complete with leather quad captains chairs). Can I assume we've decided to stick with the Mtn View Tied House? Has a time been set? I'd suggest 7pm-ish for dinner. -jrp _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
SV: Mersenne: New exponents
Title: SV: Mersenne: New exponents If you find a new prime smaller than M39, you have found something *really* rare - an out-of-order Mersenne prime. Only one of those as ever been found when Welsh and Colquitt found M110503. Some argue that M4253 was found out-of-order, but the computer discovered it in-order M61, M89, and M107 were also out-of-order. Best wishes Jan
RE: Mersenne: Re: Factoring benefit/cost ratio
On 4 Dec 2001, at 1:19, Paul Leyland wrote: From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]] (Aside - we're rather more likely to find a 75-bit factor than a 75- digit factor. In fact, finding a 75-digit prime factor of a no factors known Mersenne number with an exponent under 80 million would be a significant achievement in itself. Finding a 75-digit prime and non-algebraic factor of any integer with more than, say, 200 digits would be a significant achievement. The record today is 55 digits; it reached 53 digits 3 years ago and only a handful of factors with 50 or more digits have been found ever. I have precisely one of them to my credit 8-) Sure. Not quite the same since there appears to be no certificate of primality, but on 30 Aug 2001 there was a message on this list to the effect that M727 (c219) = prp98.prp128. So much ECM work was done on M727 (before the NFS people started work) that it is highly unlikely that there are any factors 10^50, which means that at least the 98-digit probable prime is almost certainly a genuine prime. (Maybe that's been proved by now. ECPP on general numbers of around 100 digits isn't very expensive.) I think the 55 digit record applies to ECM. A number of much larger factors (not counting cofactors) have been found using number field sieve techniques. At the moment, having found one factor, we quit. That's sufficient effort for the purpose of trying to find Mersenne primes. A little more work might break the cofactor down further. Actually, some of us don't quit. But we're a small bunch of weirdos, and we only work on tiny exponents anyway. I was speaking for the project rather than myself. I'm also one of the small bunch of weirdos. Regards Brian Beesley _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: SF Bay area GIMPS party
I'm still waiting to hear from a few people before I finalize the venue. The time is set: 6pm Friday for drinks and chit-chat, eat around 7. -Ernst _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: Mersenne Digest V1 #913
Brian Beesley wrote Ah, but George's GIMPS stats encourage factoring by removing LL testing credit when a factor is subsequently found. (Either you should have done more factoring before you started LL testing, or the factoring you did was expensive!) Okay then, I just turned this in 7213061 67 DF 168956092713627344887 04-Dec-01 13:18 labrat04 How do we confirm the original tester has now *lost* this credit? Nathan Russell wrote At 07:57 PM 12/2/2001 +, Gordon Spence wrote: A particularly sore point. If we maintained a top savers list whereby for every factor found you were credited with the time an LL test would have taken, then I and the other Lone Mersenne Hunters would pulverise these big university teams. Should George get credit for eliminating all those composite exponents when he made his initial list in the mid-1990's? Yes of course he should! He probably found over a dozen times as many composites in (at a guess) under two minutes than we'll EVER find, at least until the project is extended past 80M. The Lone Mersenne Hunters are searching right up to that limit, the only reason we don't go any higher is because the current version of Prime maxes out at 79.999M... Ernst Mayer wrote: OK, the San Francisco Bay area GIMPS get-together will take place this coming Friday, 7. December, in the south bay area (precise venue to be decided soon - see below.) Any GIMPS participant or Mersenne prime fan is welcome to join us, along with anyone else you'd like to bring - this is not a formal party.For those not coming from the San Jose area, the venue will be close to a Caltrain station, and hence should be reachable from e.g. SFO airport or other outlying areas. I'm also going to try to arrange what ridesharing I can, so if you can provide a ride or need a ride, please let me know. I looks like several folks from far-flung places will be attending, so should be a quite interesting company. Alas, Luke Welsh can't attend, but he suggested several venues, two of which form my short list. 1) Tied House, Mountain View 2) Faultline Brewery, Sunnyvale 1) is very close to a Caltrain station; 2) supposedly has very good food. I can vouch for the fact that the food is in fact excellent, and the creme caramel a speciality. Considering it's CA they make not a bad attempt at brewing beer either! Unfortunately my next visit to San Jose is not till the week before Xmas, so it's cold,wet and dark UK for me...but I'll have a virtual pint with you ;-) regards Gordon M2976221 is still the largest prime listed in Knuth by the way ;-) _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: Mersenne Digest V1 #913
TorbenS wrote No you wouldn't because they would like yourself go to do only factoring work, Only factoring work? I found over 95% of those on a single P133.. Brian Beesley wrote I've triple-checked thousands of small exponents - some of the ones where the accepted residual was recorded to only 16 bits or less, which makes the chance of an undetected error _much_ greater (though still quite small) - so far no substantive errors in the database have come to light. A very few (think fingers of one hand) instances of incorrectly matched residuals have come to light - completing the double-check in these cases proved that one of the recorded residuals was correct. Currently my team report cleared list shows 338 double checks and 12 double checked factored including this monster 6630223 87 DF 195139088771490335223859559 07-Apr-01 07:58 trilog (In fact when it was checked in PrimeNet initially rejected it because it was longer than this sort of check was supposed to find! Has anyone found a factor bigger than 87 bits using Prime95?) Of course some of these may be because the original check went to a lower bit depth than the version of Prime95 that I used. I know from doing deep factoring in the 60m range that one more bit of factoring can find a lot of extra factors...So if we say that as a ballpark figure half of these are due to an increase in factoring depth, then the error rate from this admittedly small sample is 1.78% or in other words of the current 137,924 exponents less than 20m with only a single LL test we can expect to find just under 2500 exponents with an incorrect result. regards Gordon _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: SF Bay area GIMPS party
OK, since I only received a location preference from one person (thanks, Spike!), their vote gets counted: WHAT: 3rd not-quite-annual San Francisco Bay Area GIMPS Get-together WHO: Any GIMPS member (we'll take your word for it :) or prime number enthusiast. Bring a friend/spouse /significant other/not-so-significant other WHEN: Friday, 7. December. Drinks start at 6pm, dinner@7 WHERE: Tied House Cafe Brewery 954 Villa Street Mountain View CA 650-965-2739 (see description below) * * * I was going to offer a large couch in my apartment to anyone who needs a place to stay overnight, but that's already been taken by one of the attendees who asked. If anyone else who plans to attend needs or can offer a place to stay the night, please let me know. Re. Rides: John Pierce has kindly offered rides in his new mega-mobile-SUV-kind-of-vehicle to folks from the Santa Cruz area. If you live (say) in Monterey or Pacific Grove, you'll probably want to meet him at some convenient location in SC. John says this thing even has captain's chairs, so if you want to sit in one of those, practice your 'Star Trek' phrases, you know, Make it so, Steady as she goes, Helm, Scotty, I need warp now, and so forth. (I never did figure out the first name of that Helm fellow - Matt, perhaps? :) - Peter Montgomery (assuming he can make it that evening) needs a ride from the North Bay, preferably from Marin County, but I believe he can also meet someone in San Francisco, if needed. - If anyone else needs/can share a ride, let me know. * * * Here is the venue description from citysearch.com: Restaurant Review (I've added some very minor comments of my own, enclosed in [] - EWM.) Brews We Like The Cascade Amber is the most popular, and is quite good. The Alpine Gold ale is clean in both hop aroma and finish. Look for seasonal brews such as the strong IPA [Or the M#39 Pale Ale]. Bites We Like Stay away from anything that sounds complicated (citrus shrimp, apple gorgonzola salad, [generalized Fermat primes,] et cetera). Stick with pub grub like the burgers, sausage sampler plate and the huge black bean nachos. The Look Big beer halls with tall ceilings to accommodate the huge vats full of tasty brews [and future world-record-prime posters]. The San Jose location has a particularly attractive patio area. The Crowd Young professionals mingle with serious beer snobs in a sports-fan-[and-number-theory-]friendly environment. The Critics Agree The Tied House beers have received many awards for the brews, including 13 [a Mersenne prime exponent] Great American Beer Festival medals. [tip sheet] One of Silicon Valley's Best Nominated for best brewpub for its comfortable atmosphere and quality beers. Catch a Show Grab a brew before a show. The Mountain View location is near Shoreline Amphitheatre Another Good Brewpub Try the Los Gatos Brewing Company [maybe next time.] * * * I look forward to seeing my fellow GIMPSers there! -Ernst _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: p-1 records
Gordon Spence wrote: Currently my team report cleared list shows 338 double checks and 12 double checked factored including this monster 6630223 87 DF 195139088771490335223859559 07-Apr-01 07:58 trilog (In fact when it was checked in PrimeNet initially rejected it because it was longer than this sort of check was supposed to find! Has anyone found a factor bigger than 87 bits using Prime95?) 10750127 103 F 7866348588447235992766781311399 14-Jan-01 10:57 Arnor Aries 11781977 103 F 8765843379800293878049454631169 15-Dec-00 20:06 mmesserWork_NT 11926087 103 F 8167296501437056056688534765783 07-Jan-01 10:52 rsuntagKayak_XU 12348829 103 F 9722991869324431663702571958950 22-Feb-01 07:48 SCUM C7375CE26 12423109 103 F 9668741834447195893278167681393 01-Mar-01 14:36 CamLewis work-syn-1 12469069 103 F 7539700408276934619634505308431 09-Mar-01 14:17 chbarr2Domain01 these are the first 6 I found. YotN, Henk _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: Re: Factoring benefit/cost ratio
At 06:11 PM 12/4/2001 +, [EMAIL PROTECTED] wrote: Sure. Not quite the same since there appears to be no certificate of primality, but on 30 Aug 2001 there was a message on this list to the effect that M727 (c219) = prp98.prp128. Does anyone know how much CPU time was spent? So much ECM work was done on M727 (before the NFS people started work) that it is highly unlikely that there are any factors 10^50, which means that at least the 98-digit probable prime is almost certainly a genuine prime. (Maybe that's been proved by now. ECPP on general numbers of around 100 digits isn't very expensive.) Especially when one uses Primo, which makes numbers of even a thousand digits take perhaps an afternoon on my machine. I doubt very strongly I'm the first, but just for reference: http://www.mail-archive.com/mersenne@base.com/msg06304.html http://www.acsu.buffalo.edu/~nrussell/M727.zip Nathan _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: New exponents
On 4 Dec 2001, at 11:48, Nathan Russell wrote: For the information of the list, the folks who *want* to try to get exponents below (the presumed) M#39 might want to look into manually fetching work at 2:00 (IIRC) in the morning Eastern standard (7 or 8 GMT), when the server releases exponents of folks who have stopped participating without properly quitting. The best time to get small exponents is 0601 GMT. I thought the point of the original message was that someone specifically wanted to get larger exponents. The best time to do that is 0559 GMT. You do run a risk that someone will throw back a small exponent just before you grab one, but you can always throw it back try again another day. You face a small risk that the original tester will submit a result, but even in that case you'll get credit for the double-check (though that would be a small consolation if a prime were found). This would be an interesting situation: (a) I acquire an assignment, let it expire but carry on working on it (b) You grab the assignment when it's recycled Case 1: I finish first, find a prime and announce my discovery. I did the work but the exponent is assigned to you! Who gets the credit??? Well, I suppose I _could_ grab the credit by making a public announcement without checking the result in to GIMPS/PrimeNet, but this is definitely against the spirit of the project. Conversely you hardly deserve to get the credit for a discovery which you haven't yet made. I think it's better to withhold publicity until you finish, then we can be treated as co-discoverers. Case 2: We both finish independently (it doesn't matter in which order, provided that we are not in direct contact with each other aren't aware of each other's discovery until after we have communicated the result to GIMPS/PrimeNet). This case is clear cut, we're co-discoverers. Case 3: You finish first communicate your discovery through GIMPS/PrimeNet in the usual way. This case is also clear, you're the discoverer. This probably needs to be spelled out in legal language just in case it happens in a situation where a substantial cash prize is involved (enough for it to be worthwhile paying to fight a court case). Regards Brian Beesley _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: p-1 records
At 10:28 PM 12/4/2001 +0100, Henk Stokhorst wrote: (as part of a listing of factors found by himself) 12348829 103 F 9722991869324431663702571958950 22-Feb-01 07:48 SCUM C7375CE26 Is this a bug in the reporting software? I don't have the tools to work it out exactly, but a 103-bit number should be slightly larger than 2^103, or 10141204801825835211973625643008. the factor 9722991869324431663702571958950 is one digit too short, and thus appears to be truncated. The fact that it is even, and there is a relative shortage of Mrsenne numbers wandering about with even factors (or, for that matter, factors of five) would seem to me to confirm that. However, if it were truncated it couldn't have the beginning digit 9 - then it'd have 106 bits, unless my mental math is off. Something really odd is going on. Nathan _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: New exponents
At 09:59 PM 12/4/2001 +, [EMAIL PROTECTED] wrote: This would be an interesting situation: (a) I acquire an assignment, let it expire but carry on working on it (b) You grab the assignment when it's recycled Case 1: I finish first, find a prime and announce my discovery. I did the work but the exponent is assigned to you! Who gets the credit??? You, get the credit. User b will be mighty disheartened. I know first hand. Slowinski's Cray beat my own Pentium-90 by just a few days in the discovery of M#34. As to legal issues, the disclaimer section of the download page states: We are not responsible for lost prize money, fame, credit, etc. should someone accidentally or maliciously test the number you are working on and find it to be prime. _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: Factoring benefit/cost ratio
- Original Message - From: [EMAIL PROTECTED] To: Daran [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Sent: Monday, December 03, 2001 11:22 PM Subject: Re: Mersenne: Re: Factoring benefit/cost ratio On 3 Dec 2001, at 20:45, Daran wrote: Shouldn't that be 1.015 for double-checking assignments? I think 1.03... Yes, of course. ...However you do have a point. P-1 limits do depend on the trial factoring depth,... Now I'm puzzled. Obviously both P-1 and trial factoring limits both depend upon the exponant, so will correlate, but I don't see a direct dependency between them. and are much smaller for DC assignments than for first tests, so there is already something built in. Right. I'd noticed that my P-1 probabilities for DC assignments were about half that for LLs, but I'd attributed that to the differences between the magnitudes of the exponants. This makes more sense. Also does the cost part of the calculation recognise the increased cost of trial-factorisation after 2^64? Yes. The trial factoring depth is constant at 64 bits from ~8.5 million to ~13 million. Don't forget that the number of candidates which need to be checked is _inversely_ proportional to the exponent. Because any factor must be of form 2kp+1. [...] Finally if P-1 factorisation were to be spun off into a separate work unit, then the optimal arangement would be to trial factor while cost_of_trial_factoring * chance_of_P-1_factoring is less than cost_of_P-1_factoring * chance_of_trial_factoring. Then P-1 factorise. Then complete trial factorisation according to the above formula. Interesting - but I think the effect would be small. Perhaps, but the effort to implement (without spinning off P-1 into a separate work type) would also be small. The existing formula (cost_of_trial_factoring chance_of_trial_factoring * cost_of_LL_test * 2.03) ignores the effect of P-1. A better formula would be:- cost_of_trial_factoring chance_of_trial_factoring * (cost_of_P-1_factoring + (1-chance_of_P-1_factoring)*(cost_of_LL_test * 2.03). This change on its own would surely be trivial to implement. But then, if the P-1 fails, you might as well carry on and do a little more TF, which brings us back to the simpler formula I gave earlier. You might also want to lower your P-1 bounds a shade to take into account the fact that a successful factorisation may only save a little extra TF effort. The end result is a *tiny* reduction in the probability of finding a factor (because of the slight reduction in P-1 bounds). But you'll do less work, and if you do find one, you'll probably find it earlier. How much earlier? I've just completed P-1 on M656677 which took 8787 seconds which about 1.5% of the DC estimated to take 6 days 23 hours 43 minute equals 603780 seconds, compared with a 2.6% chance of success. My guess is that this would put it optimally just before the last round of TF, which is (or should be) close to the break-even point. I'd need an estimate for the time of the last round of TF to be any more precise. The calculation would also need to be repeated for a first-time LL assignment. My final remarks on the subject of early P-1 is the observation that TF and P-1 search overlapping factor spaces. Are there any gains to be had in TF from sieving out some of the smooth k's that an early P-1 failed to find? Could you structure the factor candidate generation code, so that unsieved list doesn't contain any smooth k's in the first place? Even if it's not possible or cost effective to do either of these, the fact that there are smooth k's among the candidates should lower the estimate for the probability of success. Another reason to spin off P-1 into a separate work type is to allow machines with heaps of memory to concentrate on this kind of work. A little experimentation shows that the probability of a successful P-1 with 400MB is roughly double that of one with a minimal configuration, and some machines will be doing LLs/DCs without the ability to P-1 at all. What I envisiage is that a virgin exponant would first go out to P-1(which would also do the first few rounds of TF, according to my earlier formula), then as a factoring assignment (to completion), then finally to LL and DC. What about factoring to a fractional depth? With a roughly logarithmic distribution of factors, surely about half the factors between 2^n and 2^(n+1) would be smaller than 2^(n+0.5), whilst searching to 2^(n+0.5) would take only about 41% of the time taken to search the whole interval. This had occured to me. One could calculate the exact break-even point and TF thus far and no further. However the gains would be minimal for many exponants in the middle of the depth 'bands', which are already being near-optimally factored. Even those at the edges of the depth bands can't be very far from the break-even point. Also the server would need to record more information to enable TF to be taken a further at a later
Mersenne: Re: SF Bay area GIMPS party p.s.
p.s.: the reservation will be under the name Mersenne. pps: I was hoping to be able to bill the whole thing to the good friar's expense account, but the abbot said non to that. Guess we'll have to pay for our own beer. :( _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: p-1 records
At 05:40 PM 12/4/2001 -0500, Nathan Russell wrote: 12348829 103 F 9722991869324431663702571958950 22-Feb-01 07:48 Is this a bug in the reporting software? Something really odd is going on. Yes. The structure used to pass back factors found only supports factors up to 32 digits. The server misreports the bit-length for very large factors. You may notice that when you finish an assignment two messages are sent to the server. One is the aforementioned C structure. The other is a text message (the same text as is written to results.txt). Fortunately, I use the text messages to update my databases which has no such 32 digit limitation. The largest factor found by P-1 factoring of large exponents is 35 digits: 1318781363113922700063643342764849026462401 _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: Factoring benefit/cost ratio
- Original Message - From: [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, December 04, 2001 2:38 AM Subject: Re: Mersenne: Re: Factoring benefit/cost ratio 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? Say rather that there are various criteria by which the two projects can be compared. It's probably true that it would take them decades or more to completely factor a set of prime exponents comparable to those which GIMPS has verified composite. (and that's ignoring the effort to factorise the cofactors of Mersennes with composite exponents). They're probably not that far behind GIMPS in terms of total computing done. How far will depend upon how good they are at mobilising support. [...] 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. :) Can't argue with that. [...] 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. That seemed to be the question you were asking. [...] 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. I agree. But you can look at this in terms of an even greater project than GIMPS - The Great Distributed Computing Project that encompasses all such efforts, and aims to use spare computing cycles to increase the knowledge base of humankind generally. What contribution one chooses to make depends upon ones own personal preferences. Richard B. Woods Daran G. _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: Factoring benefit/cost ratio
- Original Message - From: George Woltman [EMAIL PROTECTED] To: [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Tuesday, December 04, 2001 3:41 AM Subject: Re: Mersenne: Re: Factoring benefit/cost ratio I think more of the discussion has centered around stats and the formula for picking how far to trial factor, rather than whether factoring is of some mathematical value... That's true, at least for my own recent contributions to this discussion. However, what I've been trying to do is float a few ideas for increasing the effectiveness of the factorising effort. If P-1 was done early, as I suggested, with bounds unchanged, then exactly the same Mersennes will get factored sooner, on average, and with less work. Ditto with the smooth k sieving idea. And if the cost of factoring is reduced, the optimal depth increases. The benefits of such an exercise are even greater if factors are given an intrinsic value of their own. Of course, the real scarce resource is not computer cycles, nor even ideas for improvement, but in programming effort to implement. Calculating that particular trade-off I leave to others. -- George Daran G. _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: New exponents
- Original Message - From: Keith Garland [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, December 03, 2001 2:53 PM Subject: Mersenne: New exponents Hi from Ireland - I have a few questions about how M39 will affect the allocation of current/new exponents. Once the result has been announced I suppose we will recommence searching above M39? No. We are looking for /all/ Mersenne primes, not just one larger than the biggest one we know. We don't know whether M#39 really is M39 or not, and the only way to find out is to test all smaller prime exponants. I got a couple of new exponents over the weekend - I assume that they are not necessarily M39 in order to maintain secrecy. If so then, after the announcement, should we dump our existing tests or finish off factoring things that are half finished? Please finish them. Does prime95 handle this scenario automatically - i.e. will new exponents be automatically sent if a manual update is done? Thanks, Keith Daran G. _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: Mersenne Digest V1 #912
- Original Message - From: Nathan Russell [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, December 03, 2001 8:29 AM Subject: Re: Mersenne: Re: Mersenne Digest V1 #912 At 07:57 PM 12/2/2001 +, Gordon Spence wrote: A particularly sore point. If we maintained a top savers list whereby for every factor found you were credited with the time an LL test would have taken, then I and the other Lone Mersenne Hunters would pulverise these big university teams. Should George get credit for eliminating all those composite exponents when he made his initial list in the mid-1990's? He probably found over a dozen times as many composites in (at a guess) under two minutes than we'll EVER find, at least until the project is extended past 80M. Don't forget all the integers that were eliminated because they weren't Mersenne numbers, the non-integral rationals, the uncountable infinity of non-rational real numbers, complex numbers, quaternians... The rest of our efforts have been trivial in comparison. :-) Nathan Daran G. _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
