Mersenne: Linux VFAT question
Hi, Jan Scheller is having a problem (see below). Are there any Linux users that can provide help? Please include Jan in your reply as Jan is not subscribed to this mailing list. I've already recommended the "poor man's" solution of having mprime not write to disk every 30 minutes. Best regards George snip But the fact is that the performance of my mounted hdd win98 (vfat) partition is very low. All my normal linux (ext2) partitions work with normal performance. If I execute a command like `ls -l /Win98` (/Win98 is the path of may win98 (vfat) partition) it takes more than a second to get the result. The second points is, that the swapping seems to be slower than without running mprime. I run mprime every time at the lowest priority. Is there possibility to rise the performance of my vfat partition while running mprime? Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Linux VFAT question
But the fact is that the performance of my mounted hdd win98 (vfat) partition is very low. All my normal linux (ext2) partitions work with normal performance. If I execute a command like `ls -l /Win98` (/Win98 is the path of may win98 (vfat) partition) it takes more than a second to get the result. The second points is, that the swapping seems to be slower than without running mprime. I run mprime every time at the lowest priority. cd to various directories, then type vdir|wc -l in each. This tells you how many files the directory has. The more files, the longer it takes to sort them. vdir -U lists the directory without sorting it, which is a little faster. mprime just writes once every 30 minutes, so whether it's running in the Windows drive or the Linux drive is inconsequential. As to the swapping, the swap daemon runs at 12 naughty, so I don't see why mprime at 20 nice would bother it at all. phma Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: A few questions
At 12:14 PM 6/27/99 -0400, Geoffrey Faivre-Malloy wrote: How large will the exponent be for a 10,000,000 digit prime number? digits x 3.32192 gives the approximate exponent. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: Statistics
There used to be a web site that showed top 100 type statistics and allowed searching on the primenet results. Does anyone have that link? G-Man Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: A few questions
At 12:14 PM 6/27/99 -0400, you wrote: How large will the exponent be for a 10,000,000 digit prime number? P will be over 33,000,000 or roughly thereabouts. I'm sure someone can give a more precise number. Has the prime number that was found a week ago been announced on this list? I.E. What number was it? George has announced that the number that was suspected prime has been confirmed to be prime by different hardware and algorithms. Because of the EFF award money rules, we "GIMPS at large" will not be permitted to know what the exponent was, or who discovered it, until an article has been published in a peer-review academic research magazine or such. George has said he is working on getting such a publication, but that no publication date has been set. If he were to announce the prime NOW, prior to publication, however, it COULD void the discoverer's claim to the prize money, so I understand the caution in talking about it. I suspect that were we to find another one between 1MM and 9.9MM digits, where no prize money was at stake, that the announcement would be more along the lines of M37 -- Slowinski or someone else confirming it, and just getting it published in a newspaper. George has frequently used the SJ Mercury News for that (in our last three discoveries).With the prize money at stake, it is different. Slovinski used to test huge numbers of primes...is he still doing that? While I don't know him from Adam, David SLOWINSKI (with a w) still works at Cray, and still uses whatever spare CPU time he can locate to hunt for primes. I *suspect* that in light of GIMPS' success, he is likely looking much higher than we are now (and has been for some time, again as a guess). He knows our current program cannot top P 20,000,000, so I suspect he's above that range, perhaps by a good margin. It may be that he breaks GIMPS record(s) again someday. I do know that the last time George expanded Prime95 to hunt up to 20MM (up from 3MM), that George sent several residues in the upper ranges to David for confirmation, and that David was able to confirm SOME of them rather quickly (faster than a Cray could do the calculations on the spot, so they were already tested). This to me indicates that David is searching the numbers far above our top potential range, especially since a Cray can test such numbers in about a week or two, as a guess. Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Linux VFAT question
On Sun, Jun 27, 1999 at 09:18:13AM -0400, George Woltman wrote: If I execute a command like `ls -l /Win98` (/Win98 is the path of may win98 (vfat) partition) it takes more than a second to get the result. The second points is, that the swapping seems to be slower than without running mprime. I run mprime every time at the lowest priority. Hmmm... I'm not completely sure if I understand the problem. Do you mean that your vfat access is slower in general when running mprime? Or just when you just have started mprime, and it's reading the p-file from disk? And what is this `swapping' you're talking about, is that disk access? (A simple but ugly solution would be storing all your mprime files (INI-files, p/q files, etc.) on an ext2 partition, and copy them to/from the vfat partition automatically on boot and reboot. (How you do this depends a bit on your distribution.) Of course, if you don't use Windows very much, you could drop `Windows support' totally.) /* Steinar */ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: Mersenne FAQ
All, Here is a potential FAQ of the mersenne mailing list. At the moment it only deals with factoring, but this should change. Any suggestions for what should be in the FAQ? Any mistakes? Any Clarifications? -Lucas Wiman Q: How is factoring done on mersenne numbers? A: We check a potential factor n of Mp by seeing if 2^p (mod n)=1 Q: But doesn't this mean using very large numbers, and computing 2^p? A: Not at all, there is a very simple algorithm for finding a^b (mod c), and here's how it works: we set res=1, then multiply res by a^(2^n) mod c whenever the nth binary digit of b is 1 a^(2^n) mod c is relativly easy to calculate through repeated sqaring of a mod c (note that for any o,p, and m, (o^p)==(o mod m)^p (mod m) where == is the "congruent to" symbol) Q: That's still a lot of factors!!! A: Well we can significantly reduce the number of factors through some simple theorems which state that: (1) any factor of 2^p-1 must be of the form 2*k*p+1 for k0 (2) any factor of 2^p-1 must be of the form 8*n+1 or 8*n-1 for n0 (3) the smallest factor (other than 1) of any number must be prime Theorem (1) reduces the number of cases to 1/(2*p) of all numbers. Theorem (2) reuduces those to 1/2 of those. Theorem (3) can reduce the factors down to only prime numbers, but that takes too much time. It is generally better simply to sieve out potential factors with very small factors. Q: But how can you sieve out small factors from potential factors? A: Well, I think an example would be most illistrative. Say we want to seive out all potential factors divisable by 3, 5, or 7. Well we can create an array of 3*5*7=105 elements, with all elements set to 1 (we'll call this array N). Then elementate all N[i] such that i is divisable by 3, 5, or 7. Then we can keep a running value of 2*k*p+1 mod 105 then if N[2*k*p+1 mod 105]=0 we skip that factor, and go on to the next one. Q: How much does all this actually help? A: The sieving for small factors (up to 17), as well as theorem (2) can can seive out about 32% of potential factors of the form (2*k*p+1). Q: Wouldn't it be more effiecient to check prime numbers and see if they divide as certain 2^p-1? A: Yes and no. It is theoretically more effiecient to do this, however this also produces uninteresting (and relativly useless) results for where p itself is composite. Q: A prime number cannot divide more than one mersenne number, so why not create a table of all the prime numbers which divide mersenne numbers so as not to duplicate work? A: This isn't really workable because it would take longer to check the table than it would to just check the factor. Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
RE: Mersenne: A few questions
George has announced that the number that was suspected prime has been confirmed to be prime by different hardware and algorithms. Because of the EFF award money rules, we "GIMPS at large" will not be permitted to know what the exponent was, or who discovered it, until an article has been published in a peer-review academic research magazine or such. George has said he is working on getting such a publication, but that no publication date has been set. If he were to announce the prime NOW, prior to publication, however, it COULD void the discoverer's claim to the prize money, so I understand the caution in talking about it. Well, the EFF has always struck me as a reasonable sort of organization, not prone to arbitrariness. Have you asked them, George, whether you can submit the exponent to them to establish precedence, then announce it publicly so we can all know what it is, and then wait for the money until after the article is published? I presume the publication requirement is a way for them to be sure the claim has been verified to be real. Payment after publishing makes some sense, but why would not being able to announce until after publishing make any sense if you've already established you knew the exponent first? Or have I completely missed some pertinent point? Robert Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: M38 in the news
http://www.oregonlive.com/news/99/06/st062601.html Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne Digest V1 #589
Mersenne Digest Sunday, June 27 1999 Volume 01 : Number 589 -- Date: Sat, 26 Jun 1999 13:59:15 -0400 From: "Geoffrey Faivre-Malloy" [EMAIL PROTECTED] Subject: Mersenne: Another factor found for Fermat 16 I found another factor for Fermat 16. What do I do now? How can I factor this number that I found? Are there programs out there that will let me do that? FYI, the factor is: M16384 has a factor: 3178457030898592746194675570663374420833971377365687459461386297851584459031 8073180374859604847822828243686877928403667633015295 G-Man Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm -- Date: Sat, 26 Jun 1999 15:58:33 -0400 From: Allan Menezes [EMAIL PROTECTED] Subject: Re: Mersenne: Distribution of Mersenne primes According to Paulo Ribenboim's book quoted below by Jud Euler's Constant gamma=0.577215665... and working out the number of mersenne primes below p=700 in Mathematica 4.0 gives 39.5572 primes, so we must be missing a prime if Wagstaffs' right. Allan Menezes Jud McCranie wrote: For those of us who don't have access to Wagstaff's 1983 paper "Divisors of Mersenne Numbers", it is nicely summarized in "The New Book of Prime Number Records", by Paulo Ribenboim, chapter 6, section V.A. (page 411-413 in this edition). He gives 3 statements: (a) The number of Mersenne primes x is about log(log(x))*e^gamma/log(2) (b) the expected number of Mersenne primes between x and 2x is about e^gamma. (equivalent to part a) (c) the probability that Mq is prime is about c*log(aq)/q where c=e^gamma/log(2) and a=2 if q = 1 mod 4; a=6 if q=1 mod 4. It gives fours considerations upon which Wagstaff's conjecture is based. Of course, these imply that the nth Mersenne number is about [2^(-gamma)]^n, or 1.4759^n. He goes on to mention Eberhart's earlier conjecture of (3/2)^n, but states that there is no serious reason supporting this version of the conjecture. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm -- Date: Sat, 26 Jun 1999 23:15:57 +0200 From: "Steinar H. Gunderson" [EMAIL PROTECTED] Subject: Mersenne: Re: [Fermat] Here is the complete factorization of your number, directly from giantint. As before, some of these factors may be composite. 3 * 5 * 17 * 257 * 641 * 65537 * 87596535553 * 12360473009170367279616001 * 6700417 * 26017793 * 63766529 * 190274191361 * 67280421310721 * 1256132134125569 * 59649589127497217 /* Steinar */ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm -- Date: Sat, 26 Jun 1999 21:33:59 GMT From: [EMAIL PROTECTED] (Steven Whitaker) Subject: Re: Mersenne: Another factor found for Fermat 16 On Sat, 26 Jun 1999 13:59:15 -0400, you wrote: I found another factor for Fermat 16. What do I do now? How can I factor this number that I found? Are there programs out there that will let me do that? FYI, the factor is: M16384 has a factor: 3178457030898592746194675570663374420833971377365687459461386297851584459031 8073180374859604847822828243686877928403667633015295 G-Man G-Man, I'm afraid I have some bad news. M16384 is not a Fermat number. It is 2^(2^14)-1 whereas a Fermat number is of the form 2^(2^n)+1. [Note the signs]. If you want to factor Fermat numbers, try P16384. However, all may not be lost. We can factorise M16384 algebraically as (2^8192+1)(2^4096+1)(2^2048+1)...(2^4+1)(2^2+1)(2^1+1) [ie F13*F12*F11...*F2*F1*F0] That means that if we remove all the known factors of these Fermat numbers from your factor, we may be left with a residue greater than 1. That must be a previously unknown factor either of F12 or F13 (all the others having only known factors). Unfortunately, as I'm not a mathematician, I don't have a factoring program that can deal with numbers of that size - but I'm sure some of the real mathematicians on the list can oblige. If you want a factorer that can handle somewhat smaller numbers, try factor.exe. You can download this from Chris Caldwell's prime pages (http://www.utm.edu/research/primes/index.html) which also contain a lot of other interesting prime-related information. Best of luck Steve 29 Mersenne factors found and counting Well, if you do find a factor of a Fermat number, Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: M38 in the news
This is a pretty good article... a few things I didn't know; someone should add a history section to the FAQ, for those of us that haven't been around too long. ;-) On the other hand, there are a few things that could be polished up in the article... to quote: "Although in theory an infinite number of primes could be found, this latest discovery is only the 38th to be verified." Close, anyway. ---Chip On Sun, 27 Jun 1999, Luke Welsh wrote: http://www.oregonlive.com/news/99/06/st062601.html Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm \\ ^ // (o o) ---oOO--(_)--OOo | Chip Lynch| Computer Guru| | [EMAIL PROTECTED] || | (703) 465-4176 (w) | (202) 362-7978 (h) | Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
