Re: Mersenne: Re: primes source
I would NOT encourage using the gpl for this, it's far too restrictive, and the fact that the security stuff isn't included in the public code would actually be in direct violation of it. I am curious, what about the GPL do you find restrictive? -Chuck -- ~~~ : WWW: http://www.silverlink.net/poke : : E-Mail: [EMAIL PROTECTED] : ~~ : Ask Mike! Aviation's response to Dear : : Abby. http://www.avstarair.com: ~~~ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Factors Everywhere
On Sat, 18 Sep 1999, Eric Hahn wrote: What I'm looking for is the following two items for *all* Mersenne numbers 2^p-1 where p is prime and p1: It can be proven that there are an infinite number of these. 1) All known factors (including, but not limited to, the smallest known factor (noted if it isn't)) 2) Largest potential factor attempted I ask that the two items are human-readable at the very least. Will Edgington maintains this information, but it may be hundreds of megabytes in size. If a website, such as Entropia, has the space it will be useful to make this database available (in many small compressed files) so that others may use it. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Factors Everywhere
What I'm looking for is the following two items for *all* Mersenne numbers 2^p-1 where p is prime and p1: It can be proven that there are an infinite number of these. Yeah, right, I knew that... I guess I should've clarified and said for all of them that the information is known :( If no information is known where p100M, then what can I do?? 1) All known factors (including, but not limited to, the smallest known factor (noted if it isn't)) 2) Largest potential factor attempted I ask that the two items are human-readable at the very least. Will Edgington maintains this information, but it may be hundreds of megabytes in size. If a website, such as Entropia, has the space it will be useful to make this database available (in many small compressed files) so that others may use it. Isn't the majority of the information he has in machine-readable format though?? I can't make much use of it, if I can't read it... Eric Hahn _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: primes source
On Sat, 18 Sep 1999, George Woltman wrote: At 03:01 PM 9/18/99 -0400, Darxus wrote: I have a question though. Why make the Linux source dependant on code which needs to be assembled under DOS, when there is an assembler for Linux (as) ? There is a ton of assembly source code. Converting it from one syntax to another would be a great deal of work - and possibly error prone. As of two years ago there was not a tool to do the conversion automatically. It would be easier to convert the source from MASM to NASM. Both use intel syntax. NASM is free and its source code available. This is a list of the object formats it supports. * bin flat-form binary files (e.g. DOS .COM, .SYS) aout Linux a.out object files aoutb NetBSD/FreeBSD a.out object files coff COFF (i386) object files (e.g. DJGPP for DOS) elf ELF32 (i386) object files (e.g. Linux) as86 Linux as86 (bin86 version 0.3) object files obj MS-DOS 16-bit/32-bit OMF object files win32 Microsoft Win32 (i386) object files oldrdfRelocatable Dynamic Object File Format v1.1 rdf Relocatable Dynamic Object File Format v2.0 ieee IEEE-695 (LADsoft variant) object file format The NASM homepage is http://www.web-sites.co.uk/nasm/index.html There are several programs that can convert between intel and gas, but usually require some help in converting. One that can convert between NASM or MASM or Gas is at http://hermes.terminal.at/intel2gas/ Though if the object file is available and can be converted, I don't see the advantage of compiling from the source. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: primes source
On Sun, 19 Sep 1999, Conrad Curry wrote: There are several programs that can convert between intel and gas, but usually require some help in converting. One that can convert between NASM or MASM or Gas is at http://hermes.terminal.at/intel2gas/ Note that this program was designed to convert from gas to nasm; conversion from nasm to gas is spotty, and the data files used needed extensive modification to even nearly get floating point in gas correct. I can make the changes available, but this program is not ready for wholesale conversion of very large amounts of Intel floating point source. jasonp _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: primes source
On Sun, Sep 19, 1999 at 03:02:34AM -0500, Conrad Curry wrote: Though if the object file is available and can be converted, I don't see the advantage of compiling from the source. The main advantage the ability to change it in any way, especially if you don't _have_ MASM at all (ie. building with free tools only). /* Steinar */ -- Homepage: http://members.xoom.com/sneeze/ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Factor of 2^(2^31-1)-1 found ($)
All (and especially Chris), Yesterday (and the day before), I went to the Illinois number theory conference. There (2nd talk of yesterday) J. P. Selfridge announced that he would give away $1000 US for any factor found of a number which ought to be prime (he provided a list). On that list was 2^(2^31-1)-1. I began searching for a factor of this number in mersfacgmp at around 12:10 Central standard time. I thought that mersfacgmp was malfunctioning, because it terminated too quickly, but I was wrong, it had found a factor! 295257526626031 divides 2^(2^31-1)-1, I have confirmed it in 3 different programs. Just to make sure that I haven't gone off the deep end, could Chris Caldwell confirm that he actually offered a prize for this number, and could the rest of you confirm that it is an actual factor? Also, Chris, I lost the sheet that had everyone's email address' at the conference, could you send me J.P. Selfridge's email address? Thank you, Lucas To guard against errors in transmitions the factor is 295257526626031 _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: Factor of 2^(2^31-1)-1 found ($
Oopsy. That should have read J. L. Selfridge -lucas _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: Factor of 2^(2^31-1)-1 found ($)
Hi Lucas Yesterday (and the day before), I went to the Illinois number theory conference. There (2nd talk of yesterday) J. P. Selfridge announced that he would give away $1000 US for any factor found of a number which ought to be prime (he provided a list). On that list was 2^(2^31-1)-1. To guard against errors in transmitions the factor is 295257526626031 p=295257526626031 I took 2, and squared it 31 times mod p. And got the result 2^(2^31)=2 mod p Congratulations Lucas, it is indeed a factor of 2^(2^31-1)-1 well done! Had it already been shown that M(M(p)) is not necessarily prime? Chris Nash Lexington KY UNITED STATES _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: primes source
It would be easier to convert the source from MASM to NASM. Both use intel syntax. NASM is free and its source code available. This is a list of the object formats it supports. if I recall correctly, the assembler code also makes extensive use of the MASM macro facilities to generate highly repetitious code sequences. Do NASM's macros work the same as MASM's? There are a lot of subtle things going on in MASM when you get into nested macros and parameter expansions and so forth. -jrp _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: primes source
On Sun, 19 Sep 1999, poke wrote: I would NOT encourage using the gpl for this, it's far too restrictive, and the fact that the security stuff isn't included in the public code would actually be in direct violation of it. I am curious, what about the GPL do you find restrictive? A programmer trying to use gpl'ed code for part of a program automatically loses his right to deside on which licence to use on the rest, that's the fundamental restriction I dislike about it. I like the general idea, but there are clauses in the licence that restricts my freedom to decide on the licence for code I developed. Note that this does NOT apply for the lgpl (L=Library), which allows linking code without forcing the licence, but Stallman has publically announced that the lgpl should not be used for future GNU libraries, because using the gpl will force more people into free software. -- Henrik Olsen, Dawn Solutions I/S URL=http://www.iaeste.dk/~henrik/ Somewhere almost out of hearing, children were at play. It was always a pleasant, lulling sound. Always provided, of course, you couldn't hear the actual words. 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: Factor of 2^(2^31-1)-1 found ($)
On Sun, 19 Sep 1999, Lucas Wiman wrote: All (and especially Chris), Yesterday (and the day before), I went to the Illinois number theory conference. There (2nd talk of yesterday) J. P. Selfridge announced that he would give away $1000 US for any factor found of a number which ought to be prime (he provided a list). On that list was 2^(2^31-1)-1. I will check with him on what he meant--I notice at least one other number on his list is already factored. I will post the revised list here as soon as I get it. Chris _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: M(M(127)) and other M(M(p))
Hi folks, After Lucas Wiman's (re)discovery of the factor of M(M(31)), I made some comment about M(M(p)), something which of course has been long known to not always be a prime whenever M(p) is. (M(M(13)) is the first counterexample and even has a factor found by Keller). Of course, the sequence that still remains unknown is 2 M(2)=3 M(3)=7 M(7)=127 M(127)=170141183460469231731687303715884105727 M(170141183460469231731687303715884105727)=??? the first five of which are prime and the nature of the last still unknown (hardly surprising!). I noticed Lucas' search found the factor of M(M(31)) reasonably quickly, a factor which isn't that large a multiple of M(31) itself. I checked Chris Caldwell's pages on this, and Curt Noll's trial-factored M(M(127)) to 5.10^50, surprisingly low considering the size of M(127) itself, I noticed many other M(M(p)) as listed in http://www.garlic.com/~wedgingt/MMPstats.txt have only been tested to very low limits indeed. I wondered why there wasn't more work done on these - though I understand it's very hard to motivate people when Guy's law of small numbers no doubt applies, but everything M(M(61)) and above is currently unknown. It would be nice to see a few more results there. Chris _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: M(M(127)) and other M(M(p))
Of course, the sequence that still remains unknown is 2 M(2)=3 M(3)=7 M(7)=127 M(127)=170141183460469231731687303715884105727 M(170141183460469231731687303715884105727)=??? Yes, this sequence is interesting, but if someone finds a way to prove/ disprove the primality of M(M(127)), I think that would be far more significant than actually proving/disproving that specific number prime. (Assuming you don't find a factor, that is). I checked Chris Caldwell's pages on this, and Curt Noll's trial-factored M(M(127)) to 5.10^50, surprisingly low considering the size of M(127) itself, I noticed many other M(M(p)) as listed in http://www.garlic.com/~wedgingt/MMPstats.txt have only been tested to very low limits indeed. The reason is relativly clear: the work of checking *even one* factor of M(M(p)) is greater than the work required for an LL test on that number. This is because of the need for p squarings modulo some number greater than M(p). I wondered why there wasn't more work done on these - though I understand it's very hard to motivate people when Guy's law of small numbers no doubt applies, but everything M(M(61)) and above is currently unknown. It would be nice to see a few more results there. I'm guessing that if a more optimized program were created, then perhaps there would be more interest. The Selfridge prize for these numbers could help. ...However, we have no way of knowing wether or not these numbers are prime, unless we find a factor. Interestingly enough, when we find the next Mersenne prime, searching for a factor of M(M(p)) might allow us to find an even bigger prime. If for example, 6*M(p)+1 divides M(M(p)), then it must be prime! Wait, that might just be the reason to search! Will only searched up to k=4 for M(M(6972593)), but if 2*k*M(p)+1 divides M(M(p)), then you've just beaten the world record! Non-Mersenne's might once again grace the top 10 list! -Lucas _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: M(M(127)) and other M(M(p))
At 08:51 PM 9/19/99 -0400, you wrote: prime, unless we find a factor. Interestingly enough, when we find the next Mersenne prime, searching for a factor of M(M(p)) might allow us to find an even bigger prime. If for example, 6*M(p)+1 divides M(M(p)), then it must be prime! Which one must be prime? 6*M(p)+1, or M(M(p))? And why? Enquiring minds, and all Thanks! Wait, that might just be the reason to search! Will only searched up to k=4 for M(M(6972593)), but if 2*k*M(p)+1 divides M(M(p)), then you've just beaten the world record! Non-Mersenne's might once again grace the top 10 list! An interesting concept -- what sort of time factor would it take to prove such a thing with an average computer? _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: M(M(127)) and other M(M(p))
even bigger prime. If for example, 6*M(p)+1 divides M(M(p)), then it must be prime! Before anybody gets overexcited at the last posting... It is TRUE that if 2k.M(p)+1 divides M(M(p)), M(p) is prime, and k2M(p)+2, then 2k.M(p)+1 is prime. However, unless I'm mistaken, non-divisibility does not prove compositeness. You could walk past a prime (in fact, you'd expect to walk past several) and you'd never know... Chris _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: M(M(127)) and other M(M(p))
Hi there Lucas... The reason is relativly clear: the work of checking *even one* factor of M(M(p)) is greater than the work required for an LL test on that number. This is because of the need for p squarings modulo some number greater than M(p). Yes, however there is a rather curious combination of effects going on when testing these numbers. To test if x is a factor of M(M(p)) requires p squarings mod x, but p is a little less than log2(x). Admittedly, we're only testing for factors, but there's a curious side effect of the test... prime, unless we find a factor. Interestingly enough, when we find the next Mersenne prime, searching for a factor of M(M(p)) might allow us to find an even bigger prime. If for example, 6*M(p)+1 divides M(M(p)), then it must be prime! Oh, you can do much better than that... Let q=M(p), a prime. Now any factor of M(q) is of the form 2kq+1. Provided 2kq+1(2q+1)(2q+1), ie k2q+2, if 2kq+1 divides M(q), then 2kq+1 is prime. In theory then this sort of factor test can prove the primality of a number up to TWICE THE SQUARE of M(p), yet the proof still only requires only p squaring operations (admittedly, to a slightly less pleasant modulus, but readily optimizable). Of course, the downside is, one has no idea how far you'd need to search (or even if such a number exists, M(M(p)) could be prime and you'd never know it) - the upside is, you might get lucky very quickly... Wait, that might just be the reason to search! Will only searched up to k=4 for M(M(6972593)), but if 2*k*M(p)+1 divides M(M(p)), then you've just beaten the world record! Non-Mersenne's might once again grace the top 10 list! Steady on, there are a few non-Mersennes hanging on in there :) But this form is very reminiscent of the Miller/Wheeler record (the first one of the electronic age), 180.M(127)^2+1. I for one wouldn't object to dedicating a few cycles here and there to find a factor of M(M(1257787)) and who knows, find the largest known non-GIMPS prime... Chris _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: GIMPS client output
From: Darxus Iteration: 164000 / 8410531 [1%]. Clocks: 115665753 = 0.496 sec. Might be nice to display the percentage out to an accuracy that changes every hundred iterations. If you're using version 19, add "PercentPrecision=3" to the prime.ini file. If you want more than three decimal places, change the number...I believe it'll go up to six. I believe that four should be sufficient as even M33219281 changes every three or four hundred iterations with three places displayed. Rick. -+--- [EMAIL PROTECTED] http://www.alienshore.com/ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: GIMPS client output
Might be nice to display the percentage out to an accuracy that changes every hundred iterations. Hmm, looks like that's an integer of the percentage, not rounded. Guess it doesn't matter. For the one I'm working on it looks like 3 decimal places would be needed to see a change every 100 iterations. This is changed in V19 (currently in Beta). I believe (George correct me if I'm wrong) that you can specify it up to 6 decimal places. -Lucas _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: GIMPS client output
Iteration: 164000 / 8410531 [1%]. Clocks: 115665753 = 0.496 sec. Might be nice to display the percentage out to an accuracy that changes every hundred iterations. Hmm, looks like that's an integer of the percentage, not rounded. Guess it doesn't matter. For the one I'm working on it looks like 3 decimal places would be needed to see a change every 100 iterations. v19 allows this by manually adding 'PercentPrecision=' to the PRIME.INI file (Prime95 must be stopped and exited before editing, and then restarted). The valid range after the '=' is 0 to 6, therefore you can have it say: Iteration: 164000/8410531 [1.949936%]. Per iteration time: 0.496... Iteration: 164100/8410531 [1.951125%]. Per iteration time: 0.496... Mind you, even at the limit of v19 (79.3M), setting it to a value of 4, and having screen outputs at every 100 iterations, will still cause the value to increase (although by 0.0001%) Eric Hahn P.S. At the 79.3M range, you'll probably not want to set it at 100 iterations... Per iteration time on 266MHz PII with 64MB RAM is 58.781 seconds!!! (Yes, it's true, but I'm also just checking to see if anybody's awake :)) _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: GIMPS client output
From: Eric Hahn P.S. At the 79.3M range, you'll probably not want to set it at 100 iterations... Per iteration time on 266MHz PII with 64MB RAM is 58.781 seconds!!! The only question that comes to mind is if you had to plough through factoring before you got to the LL test...but then I realise that you still wouldn't be done if that were true. I signed up for an exponent in the 33mil range and the factoring alone took 13 days on a P3-500. I'd originally does it for testing purposes, but after that I've just got to let it continue. :-) In a year's time, I'd love to see some numbers on how many signed up for tem million digit numbers and later quit for smaller exponents... Rick. -+--- [EMAIL PROTECTED] http://www.alienshore.com/ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
