Mersenne: Q:GIMPS freezes my system
Hi there, I've experienced a problem. I'm wondering if anyone else has had this problem: GIMPS freezes my system after it runs for about 24 hours or so. I have Windows NT 4.0 (SP5) Dual Intel Celeron 433Mhz (BP6 motherboard) 128MB RAM If I quit both GIMPS processes on my machine (and I'm running one with the -A2 command-line option) and start them again, no problems. It's only after both have been running for some time. But I don't want to do this because I leave my computer for days at a time. Is there a work-around i can use? I've experimented with the AT WinNT task-scheduler, but I can't get the GIMPS command-line option -Tdd:hh:mm to work. Has this been implemented? Thanks in advance, Dennis __ Get Your Private, Free Email 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: Q:GIMPS freezes my system
On Mon, 24 Jan 2000, Dennis Peter wrote: Hi there, I've experienced a problem. I'm wondering if anyone else has had this problem: GIMPS freezes my system after it runs for about 24 hours or so. I have Windows NT 4.0 (SP5) Dual Intel Celeron 433Mhz (BP6 motherboard) 128MB RAM Hi Dennis, How sure are you that the prime search program is the culprit here? There have been a slew of posts to the Abit USENET newsgroup, as well as a whole lot of discussion at www.bp6.com, about problems with the BP6 randomly freezing. People running GUI operating systems on it seem to be reporting much more difficulty than those running something like Linux in text mode. I'm running a BP6 with dual Celeron 400's, and since I switched it over to running RedHat 6.0 in console mode (no XWindows), it's been the picture of stability (it is always up running 2 instances of mprime unless I bring it down for new hardware). I'm not saying that the prime search program (Prime95?) you're using isn't the problem, just that the BP6 seems to have some "stability issues" in general. Kel _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Size of largest prime factor
Pierre Abbat wrote: If I pick a huge number n at random, how much smaller than n, on average, is its largest prime factor? Jud McCranie wrote:- On the average, the largest prime factor of n is n^0.6065, and the second largest is n^0.2117. Reference: Knuth, the Art of Computer Programming, vol 2, section 4.5.4. But for Mersennes this might not be the case. For the size of exponents that we deal with Mersennes are less composite than a random set of ones zeroes. There are many reasons for this, if 2^p-1 has any factors they must be bigger than p. They must be +-1 mod 8 etc. Looking at the string of ones it certainly has regularity. Indeed there is a measure for it, the order of 2 mod 2^p-1 which is very low, =p; and any factors have this order as well. This is not average. This is not new news to most people here, but I have to remind myself, it still hasn't been proved whether there are an infinite number of Mersenne Primes or an infinite number of Mersenne composites. Cheers, Paul Landon _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Q:GIMPS freezes my system
Kel, I have run other numerous programs (including other number crunching spare CPU-cycle programs) and my system has never froze until I ran Prime95.exe. I installed GIMPS 7 days ago. I've had my system for about a year or so. I'll check out bp6.com... and yes, I know that the dual-celeron config isn't officially supported by Intel. -Dennis Original Message Follows From: "St. Dee" [EMAIL PROTECTED] To: Dennis Peter [EMAIL PROTECTED] CC: [EMAIL PROTECTED] Subject: Re: Mersenne: Q:GIMPS freezes my system Date: Mon, 24 Jan 2000 05:47:09 -0500 (EST) On Mon, 24 Jan 2000, Dennis Peter wrote: Hi there, I've experienced a problem. I'm wondering if anyone else has had this problem: GIMPS freezes my system after it runs for about 24 hours or so. I have Windows NT 4.0 (SP5) Dual Intel Celeron 433Mhz (BP6 motherboard) 128MB RAM Hi Dennis, How sure are you that the prime search program is the culprit here? There have been a slew of posts to the Abit USENET newsgroup, as well as a whole lot of discussion at www.bp6.com, about problems with the BP6 randomly freezing. People running GUI operating systems on it seem to be reporting much more difficulty than those running something like Linux in text mode. I'm running a BP6 with dual Celeron 400's, and since I switched it over to running RedHat 6.0 in console mode (no XWindows), it's been the picture of stability (it is always up running 2 instances of mprime unless I bring it down for new hardware). I'm not saying that the prime search program (Prime95?) you're using isn't the problem, just that the BP6 seems to have some "stability issues" in general. Kel __ Get Your Private, Free Email 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: Size of largest prime factor
On Mon, 24 Jan 2000, Paul Landon wrote: Subject: Re: Mersenne: Size of largest prime factor Pierre Abbat wrote: If I pick a huge number n at random, how much smaller than n, on average, is its largest prime factor? Jud McCranie wrote:- On the average, the largest prime factor of n is n^0.6065, and the second largest is n^0.2117. Reference: Knuth, the Art of Computer Programming, vol 2, section 4.5.4. But for Mersennes this might not be the case. For the size of exponents that we deal with Mersennes are less composite than a random set of ones zeroes. There are many reasons for this, if 2^p-1 has any factors they must be bigger than p. They must be +-1 mod 8 etc. Looking at the string of ones it certainly has regularity. Indeed there is a measure for it, the order of 2 mod 2^p-1 which is very low, =p; and any factors have this order as well. This is not average. This is not new news to most people here, but I have to remind myself, it still hasn't been proved whether there are an infinite number of Mersenne Primes or an infinite number of Mersenne composites. Erhm? 2^n-1 where n is composite is in itself composite, so showing that there are infinitely many Mersenne composites is easy. :) Cheers, Paul Landon -- Henrik Olsen, Dawn Solutions I/S URL=http://www.iaeste.dk/~henrik/ `Can you count, Banjo?' He looked smug. `Yes, miss. On m'fingers, miss.' `So you can count up to ...?' Susan prompted. `Thirteen, miss,' said Banjo proudly. Terry Pratchett, Hogfather _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Size of largest prime factor
Hiya Henrik, I did mean for 2^p-1; p prime. That's why I work in Computing not the discipline of Maths :-) I am certain that the graph in Knuth sect 4.5.4 (which by luck I had only read for the first time last night) is definately not applicable to Mersenne numbers (with prime exponent). I am certain that there is a minimum size for any divisor of a Mersenne (conversely there is a maximum order of 2 mod f for a candidate factor f) such that there is therefore a maximum size for the largest factor. This makes the cumulative frequency graph hit 1.0 before 100%! (I had best be precise so that one day I grow up to be a good Mathematician, - ignoring the factorisation 1 itself). Can we do some statistics on the (complete) factorisations we already have? I am also sure that in many other ways Mersennes do not behave like random numbers as discussed in sect 4.5.4. I think I am correct in what I meant to say, that it hasn't been proved that there are an infinite number of Mersenne Primes or an infinite number of Mersenne's with prime exponent that are composite or both with a limiting ratio. Thanks Henrik for encouraging me to be precise in the presense of real Mathematicians. Cheers, Paul Landon Henrik Olsen wrote: On Mon, 24 Jan 2000, Paul Landon wrote: Subject: Re: Mersenne: Size of largest prime factor [snip] This is not new news to most people here, but I have to remind myself, it still hasn't been proved whether there are an infinite number of Mersenne Primes or an infinite number of Mersenne composites. Erhm? 2^n-1 where n is composite is in itself composite, so showing that there are infinitely many Mersenne composites is easy. :) _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Size of largest prime factor
At 11:48 AM 1/24/00 +0100, Paul Landon wrote: On the average, the largest prime factor of n is n^0.6065, But for Mersennes this might not be the case. For the size of exponents that we deal with Mersennes are less composite than a random set of ones zeroes. That's right, but the original question just said a large random number. ++ | Jud McCranie | || | 137*2^197783+1 is prime! (59,541 digits, 11/11/99)| | 137*2^224879+1 is prime! (67,687 digits, 1/00)| ++ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re : Odd's on finding a factor
Dave Mullen wrote: >Sorry, I'm no mathematician, and new to the Mersenne field. > >> No, in the x-y bit range (remember that n bit integers are >> about >2^n) the first factor could be x/2 to y/2 bits long >> (powers of a power >multiply). > >What I was trying to say in my disjointed way was ... > >(Example) M11 = 2047 (11 bits long). Now 2047 has only 2 factors >(23 >x 89) and the square root of 2047 is approx 45. 45 is 6 bits >long, therefore the factor lower than the square root must have >= 6 bits, >and the factor higher than the square root must have >>=6 bits. > >23. is 5 bits long, and 89 is 7 bits long. > >Thus for the exponent 1165 bits long, if it only has 2 factors , >then the first factor must be between 2 and 3413 bits long, and >the second factor must be between 3413 and 1164 bits long. >Note that the bit lengths of the 2 factors added together must >equal the bit length of the Prime (or bit length of the >Prime + 1) !! There only a slight error with your logic... For the exponent 1165, the root is *not* 3413 bits long, but more like 5825000 bits long. Perhaps you forgot exponents add, not multiply. For simplication: 2^3 * 2^3 = 2^6 8 * 8 = 64 Therefore: 2^1165 = 2^5825000 * 2^5825000 Eric Hahn _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Size of largest prime factor
On 24 Jan 00, at 11:48, Paul Landon wrote: This is not new news to most people here, but I have to remind myself, it still hasn't been proved whether there are an infinite number of Mersenne Primes or an infinite number of Mersenne composites. The latter conjecture looks very, very probable! Note that it would be sufficient to prove that there are an infinite number of Sophie-Germain primes, since there is a "well known" theorem which states that, if p is a Sophie-Germain prime, then 2^p-1 is divisible by 2p+1. Of course, we do have heuristics which tend to indicate that the number of Mersenne primes is infinite. If this is not so, then the number of Mersenne composites _must_ be infinite. The same heuristics (or even just application of the Prime Number Theorem) suggest that the probability that 2^p-1 is prime decreases with increasing p, which is a strong indication that there are, indeed, an infinite number of Mersenne composites. The contrary would be amusing - if there are a finite number of Mersenne composites, there must be an integer P which is the exponent of the _largest_ composite Mersenne number, i.e. 2^(P+k)-1 is prime for every positive integer k. The challenge then would not be to find all the Mersenne primes, but to determine the value of P. Regards Brian Beesley _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re : Odd's on finding a factor (part 2)
Thus for the exponent 1165 bits long, if it only has 2 factors , then the first factor must be between 2 and 3413 bits long, and the second factor must be between 3413 and 1164 bits long. Note that the bit lengths of the 2 factors added together must equal the bit length of the Prime (or bit length of the Prime + 1) !! No, if the exponent=1165 (I think this is what you mean), the mersenne number must be this number of bits (as you know). The first factor must be less than sqrt(M_p), not M_(sqrt(p)), which is what you were doing. The first factor must therefore be less than 2^(p/2)=2^58250002^sqrt(1165)~=2^3413. You would probably get better results with Will Edgington's mersfacgmp program, and DJGPP (a port of g++ to dos). I'll check it out. I'm using UBASIC because for testing factors of large Mersenne, I don't need to actually represent the full Mersenne Prime. If you're familiar with UBASIC try ... Result = MODPOW(2,MersenneExponent,TrialFactor) where TrialFactor is the MersenneExponent * 2 * (some k in range 1 to 2^16) + 1. If Result = 1 then TrialFactor divides the Mersenne Prime. As UBASIC can handle around 2600 decimal digits, in theory (and with a lot of time), I could check all factors up to 2600 decimal digits for any given exponent. It's a damn sight faster than filling 16MB+ of memory with 1's and then trial dividing. Will's program does this also (see Knuth volume II (I think 4.5.3, but I'm not sure don't have my copy handy), or the mersenne FAQ at the bottom of this message). Thinking on it in a slightly more awake state, I'm not sure how much faster it would be, but try it anyway. You will need to download DJGPP (search altavista for DJGPP), set it up, compile the GMP library (ftp://metalab.unc.edu/gnu/gmp (I think), there is a dos batch file), and compile Will's program (I think it is in the links section of the mailling list FAQ). But, under windows, would George's program be the fastest (or are you using very large exponents?) Have fun, Lucas Wiman _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Q:GIMPS freezes my system
Hi there, I've experienced a problem. I'm wondering if anyone else has had this problem: GIMPS freezes my system after it runs for about 24 hours or so. I have Windows NT 4.0 (SP5) Dual Intel Celeron 433Mhz (BP6 motherboard) 128MB RAM If I quit both GIMPS processes on my machine (and I'm running one with the -A2 command-line option) and start them again, no problems. It's only after both have been running for some time. But I don't want to do this because I leave my computer for days at a time. It sounds like you might have problems with overheating in the case which can often cause lockups, since Prime95 stresses the CPU more, it produces more heat. I would advise getting a case fan. Just my $0.00 (the GNU version) -Lucas _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Round off error = 0.5
Hi all, I'm running Prime95 on a PII-400 for 6 days (no overclocking) at exponent 9409271. It's produced several outputs concerning ROUND OFF ERRORS - the last one is ROUND OFF [0.5] 0.4 What to do now? Restart from iteration 1? Regards Dieter Schmitt
Re: Mersenne: Round off error = 0.5
Hi, At 01:04 AM 1/25/00 +0100, Dieter Schmitt wrote: I'm running Prime95 on a PII-400 for 6 days (no overclocking) at exponent 9409271. It's produced several outputs concerning ROUND OFF ERRORS - the last one is ROUND OFF [0.5] 0.4 What to do now? Restart from iteration 1? The first thing to do is try and figure out if your CPU is overheating or you have some flaky memory chips. You almost certainly have a hardware problem of some type. Prime95 will go back to the last good save file after the error. So there is a chance your result is OK. The question is "did a hardware error go undetected?" I have little hard data on this, but I'd guess several errors of this type mean you have less than a 50-50 chance of producing a good result. Regards, George _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Red Red Red
Aaaack! Who's the one sending mail to the list that makes it appear with a red background? Stephan "Retinal Afterimage" Lavavej _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: Odd's on finding a factor (part 2)
Dave Mullin wrote: Result = MODPOW(2,MersenneExponent,TrialFactor) where TrialFactor is the MersenneExponent * 2 * (some k in range 1 to 2^16) + 1. If Result = 1 then TrialFactor divides the Mersenne Prime. As UBASIC can handle around 2600 decimal digits, in theory (and with a lot of time), I could check all factors up to 2600 decimal digits for any given exponent. It's a damn sight faster than filling 16MB+ of memory with 1's and then trial dividing. Ubasic can indeed handle integers up to around 2600 digits, but modpow() needs to hold intermediate results, so will only work up to around 1300 digits input. Good luck anyway! Andy Steward _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Odds on finding a factor ?
- Original Message - From: Lucas Wiman [EMAIL PROTECTED] I think under windows that dos windows only run when they are "up". (I could be wrong, I've stopped using windows again) No. You can set a background priority. In Win 95, right-click on the icon, then click "Properties". Click on the "Misc" tab and move the slider for "Idle Priority" anywhere you want between Low and High. Click "OK". If I'm going to be away from a machine for a while, I quite often set a "B" priority task running in a Ubasic window and minimise it, then run an "A" priority task running in an active window. That way, I ensure that the machine won't be idle if the "A" task completes before my return. The downside is the reduction in resources available to the "A" task while both are running. HTH, Andy Steward Factorisations of 57,619 Generalised Repunits at: http://www.users.globalnet.co.uk/~aads/index.html _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: Odds on finding a factor
There only a slight error with your logic... For the exponent1165, the root is *not* 3413 bits long, but more like 5825000bits long. Perhaps you forgot exponents add, not multiply. Okay, next time I'll open my mouth a little wider, so I can fit both feet inside. Sorry all, sometimes I put my mouth in gear before my brain is engaged. Who needs to? I have code which tries any number up to 2^95 as a factor of a Mersenne number with an exponent up to approx. 600 million, using less than 1 KByte of code space and 32 bytes of data storage. It executes in a time proportional to the logarithm of the exponent - for an exponent around 35 million, it takes approximately 2000 CPU clocks i.e. 4 microseconds per test on a 500 MHz CPU. My UBASIC is running thus :- In 36 hours, tested 88855 exponents with all multipliers 1 to 2357. (and found factors for 8860 of the exponents). 88855 exponents x 2358 multipliers = 20952090 tests = 1616 tests per second = 618 microsecs per test on a P133. Brian, I'd be very interested in a copy of that code, if you'd care to E-Mail it. Regards Dave Mullen
Re: Mersenne: Re: Odds on finding a factor
Who needs to? I have code which tries any number up to 2^95 as a factor of a Mersenne number with an exponent up to approx. 600 million, using less than 1 KByte of code space and 32 bytes of data storage. It executes in a time proportional to the logarithm of the exponent - for an exponent around 35 million, it takes approximately 2000 CPU clocks i.e. 4 microseconds per test on a 500 MHz CPU. This is a bit misleading, more accuratly, it runs in time proportional to lg(p)*lg^2(n), where p is the exponent, and n is the potential factor. Just call me "Mr. Pedantic". :) -Lucas Wiman _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne Digest V1 #683
Mersenne DigestSunday, January 23 2000Volume 01 : Number 683 -- Date: Sat, 22 Jan 2000 11:35:38 -0800 From: Gerry Snyder [EMAIL PROTECTED] Subject: Mersenne: Best chance to make a "real" contribution? Hello, Mersenners; First of all, let me say that it is a thrill to be helping in the GIMPS. Getting more computing power for the search is the main reason my new linux system is a dual Celeron rather than a single. If all I ever do is LL tests of non-primes, that will be fine. That helps the cause, and I have no expectation of finding a prime. But finding a factor (or another factor) of a Mersenne number would seem more real. Is there any significant probability that two 500 MHz Celerons and one 333 MHz Celeron could accomplish such a feat in a couple of years? Just thought I'd ask. Thanks for any help, Gerry - -- mailto:[EMAIL PROTECTED] Gerry Snyder, AIS Symposium Chair Region 15 Ass't RVP, JT Chair Member San Fernando Valley, Southern California Iris Societies in warm, winterless Los Angeles _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers -- Date: Sat, 22 Jan 2000 15:14:51 -0500 From: George Woltman [EMAIL PROTECTED] Subject: Re: Mersenne: Best chance to make a "real" contribution? Hi Gerry, At 11:35 AM 1/22/00 -0800, Gerry Snyder wrote: First of all, let me say that it is a thrill to be helping in the GIMPS. Welcome aboard! Getting more computing power for the search is the main reason my new linux system is a dual Celeron rather than a single. The second processor is a cheap way to add horsepower. It will help on many other computing tasks. An excellent decision. But finding a factor (or another factor) of a Mersenne number would seem more real. Finding new factors isn't hard. Over half of the candidates are eliminated by finding a factor rather than the expensive LL test. GIMPS by default assigns slower machines to do the factoring work. Thus, it is not uncommon for powerful machines to always get LL assignments and never find a factor. If you want the thrill of finding a factor, ask one of your CPUs to get factoring work only (the Test/Primenet dialog box). You can change this setting back at a later time. Finding new factors of small Mersennes, so called Cunningham factors, is getting more difficult. ECMNet and GIMPS have picked off most of the "easy" factors. I have two CPUs running ECM full-time. The last Cunningham factor I found was last summer. I do occasionally find new factors of medium-sized (1200 to 10) Mersenne numbers. In any event, choose the type of work you find most interesting. The goal here is to have fun while contributing to math research. Best regards, George _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers -- Date: Sat, 22 Jan 2000 15:44:16 -0500 From: "St. Dee" [EMAIL PROTECTED] Subject: Re: Mersenne: Best chance to make a "real" contribution? At 15:14 01/22/2000 -0500, George Woltman wrote: Finding new factors isn't hard. Over half of the candidates are eliminated by finding a factor rather than the expensive LL test. GIMPS by default assigns slower machines to do the factoring work. Thus, it is not uncommon for powerful machines to always get LL assignments and never find a factor. This brings up something I've been wondering about. I have a dual Celeron setup running 2 instances of mprime under Linux. With both processors crunching on LL tests, I get iteration times for each processor of around .263 for exponents around 899 (where they are presently cranking). However, if one of them factors while the other does LL testing, the processor doing the LL testing takes about .220 seconds per iteration, while the one factoring also shows a factoring speed more consistent with the speed I would expect for the processor speed. My question is: Do I get more "work" done by having both doing LL testing, or would this box contribute more to the effort by having one CPU performing factoring while the other does LL testing? Thanks! Kel, coming up on 4 years of hunting for Mersenne primes _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers -- Date: Sat, 22 Jan 2000 17:24:22 -0500 From: Foghorn Leghorn [EMAIL PROTECTED] Subject: Mersenne: Factoring beyond ECM I'm interested in trying to factor composite numbers with 100 to 200 digits. ECM becomes impractical for numbers without any factors below 50 digits or so. I have heard of
