Mersenne Digest Sunday, September 19 1999 Volume 01 : Number 628 ---------------------------------------------------------------------- Date: Fri, 17 Sep 1999 19:42:05 -0700 From: Greg Hewgill <[EMAIL PROTECTED]> Subject: Re: Mersenne: v19 DNS(?) crash... On Fri, Sep 17, 1999 at 07:57:06PM +0300, Jukka Santala wrote: > "Contacting PrimeNet Server", hangs up there for a while and then > crashes with Application Error "The exception unknown software exception > (0x000006ba) occured in the application at location 0x77e1fc45". You might have better luck using HTTP communications rather than RPC (the error 0x6ba is a Win32 RPC error). The HTTP method is the preferred method anyway, from what I've read. It's more robust and less likely to crash. Greg Hewgill _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 17 Sep 1999 23:08:19 -0400 From: Brian Beuning <[EMAIL PROTECTED]> Subject: Re: Mersenne: P-1 Thanks for the "p-1 for dummies" e-mail. Starting from this definition of the "p-1" method (I changed p to q). Discover prime factors q of a given large (mersenne) number N, when all prime factors of q-1 are "small". But as everyone on this list knows, any factor of a Mersenne number looks like 2*k*p+1 for N=2^p-1. Plugging this into the above equation gives q=2*k*p+1 q-1=2*k*p (It has been too many years since my last math class, so go easy OK?) Doesn't this mean the lower bound on a "p-1" method search should be greater that the Mersenne exponent (the p in 2^p-1) to have the best chance of success? Then the "upper bound" of the "p-1" search can be resevered for cracking a big factor in the "k" of a Mersenne factor. Brian Beuning _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 18 Sep 1999 01:09:16 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: Re: Mersenne: P-1 > But as everyone on this list knows, any factor of a Mersenne > number looks like 2*k*p+1 for N=2^p-1. Plugging this into > the above equation gives > q=2*k*p+1 > q-1=2*k*p Correct. > Doesn't this mean the lower bound on a "p-1" method search should > be greater that the Mersenne exponent (the p in 2^p-1) to have the best > chance of success? Then the "upper bound" of the "p-1" search can > be resevered for cracking a big factor in the "k" of a Mersenne factor. No. Simply multiply the exponent on the base by p. This produces the desired result, without having to go to the extra effort of extending the bound that far. I probably should add a section on P-1 to the FAQ. - -Lucas _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 18 Sep 1999 08:21:15 +0200 From: Petri Holopainen <[EMAIL PROTECTED]> Subject: Re: Mersenne: G4: real or hype? [EMAIL PROTECTED] wrote: > > - "It is 3 times faster then the PIII 600Mhz." Based on what? Give us some > SPECint or SPECfp figures that support this before making such claims. The > only datum provided (below) indicates a speedup of 1.45x, far less than 3x. > Apple is really blowing this G4 hype out of proportions. It is a really nice chip, but looking at the SPEC numbers: http://www.mot.com/SPS/PowerPC/products/semiconductor/cpu/7400.html ... they show that it's basically a G3 + Altivec and a nice FPU: CPU SPECint95 SPECfp95 - ----------- --------- -------- G3-450 21.4 13.8 G4-450 21.4 20.4 P3-550 22.3 15.1 P3-600 24.0 15.9 Athlon-550 25.1 20.6 Athlon-650 29.4 22.4 Alpha EV67-667 37.5 65.5 So this "128-bit 1 Gigaflops supercomputer" is just a load of Apple marketing propaganda (yeah, Intel does this crap too, remember "more vibrant colors" with MMX and "enhanced Internet experience" with SSE...). - -- Petri H. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 18 Sep 1999 14:42:17 +0200 From: "Lars Lindley" <[EMAIL PROTECTED]> Subject: Mersenne: v19 manual workdodo.ini error. Hi all. This monday I to my delight installed v19 and noticed a nice ~10% decrease in per-iteration time. Good work George! :) Now I ran into a bit of a strange situation. I discovered a lost exponent in the team-report and thought I would reassign that exponent for myself. I manually edited the worktodo.ini by adding the row DoubleCheck=3393469,61 on the first line. I thought that prime95 would put the exponent I was working on on hold to do the doublecheck first as v18.1 would have. To my surprise it continued with the old exponent. When I checked the status it reported it was working on the doublecheck and would be finished with that one on Sep. 22. It reported to be finished with my other exponent on Oct. 7. Strange indeed. Any input? /Lars _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 18 Sep 1999 00:39:00 -0400 From: "Chris Nash" <[EMAIL PROTECTED]> Subject: Re: Mersenne: P-1 Hi folks > Thanks for the "p-1 for dummies" e-mail. > But as everyone on this list knows, any factor of a Mersenne > number looks like 2*k*p+1 for N=2^p-1. Plugging this into > the above equation gives > q=2*k*p+1 > q-1=2*k*p > Doesn't this mean the lower bound on a "p-1" method search should > be greater that the Mersenne exponent (the p in 2^p-1) to have the best > chance of success? Then the "upper bound" of the "p-1" search can > be resevered for cracking a big factor in the "k" of a Mersenne factor. This is a great point, one that I stopped a little way short on. Indeed the 'p-1' method constructs a large product of small primes, that you're hoping will be a multiple of q-1. Since we know q-1 is a multiple of 2p, it makes sense for us to start the p-1 method not at some base a, but at a^(2p). And as you point out, the upper bound then is in fact an upper bound on the factors of k. Provided we search as far as the factors of the unknown k, we will succeed. Starting at a^(2p) is relatively a small calculation, and saves us having to wait until the P-1 method includes p in the exponentiation (it's highly unlikely we would discover one before). Of course, its possible that even so, we may not find a factor, but it makes sense to include as much as we know about the factors at the very start of the method. Alternatively, we could specify p as a lower bound - something which is probably a good idea anyway, the calculation of a P-1 factoring is then comparable to a primality test. Going to a P-1 limit of 'p' certainly covers all factors with k<=p, and many others besides. The factors that aren't covered are those with a prime or prime power factor of k above the P-1 limit. That can help you make a good guess as to how efficient your factoring attempt has been, of course, do not forget it is also possible to save the result of a P-1 attempt, return later, and "exponentiate some more" to increase the upper bound. Chris _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 18 Sep 1999 15:01:43 -0400 (EDT) From: Darxus <[EMAIL PROTECTED]> Subject: Mersenne: primes source I used to really like distributed.net. The fact that they're still, to my knowledge, only cracking encryption, and have not followed through on their plans to do OGR & primes, combined with the fact that their code is not opensourced, bother me. I've just switched to the GIMPS. 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) ? Also, the source seems to be released something like "feel free to use this code to make the world a better place as you see fit", but doesn't actually have a license. I would incourage you to release it under either the GNU General Public License (http://www.gnu.org/copyleft/gpl.html), or if you want to allow commercial use, the BSD license (which I'm significantly less familiar with). __________________________________________________________________ PGP fingerprint = 03 5B 9B A0 16 33 91 2F A5 77 BC EE 43 71 98 D4 [EMAIL PROTECTED] / http://www.op.net/~darxus Far Beyond Reason _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 18 Sep 1999 15:05:35 -0400 (EDT) From: Darxus <[EMAIL PROTECTED]> Subject: Mersenne: Debian / RedHat packages ? There doesn't appear to be a Debian package, and I've seen no reference to a RedHat package. Are there any plans to do these ? Would probably increase participation among Linux users.... __________________________________________________________________ PGP fingerprint = 03 5B 9B A0 16 33 91 2F A5 77 BC EE 43 71 98 D4 [EMAIL PROTECTED] / http://www.op.net/~darxus Far Beyond Reason _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 18 Sep 1999 22:42:13 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Mersenne: Re: primes source On Sat, Sep 18, 1999 at 03:01:43PM -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) ? gas (which is the assembler Linux uses) uses a format quite differently from NASM. One thing is the reversal of args and other problems, like: mov [eax+ebx*4+4],4 (Intel syntax) becomes movl $4,4(%eax,%ebx,4) (AT&T syntax) As you can see, converting will be a problem. I've done some of it though, so if there is an interest, I might release my converter program to the public. >I would incourage you to release it under either >the GNU General Public License (http://www.gnu.org/copyleft/gpl.html), or >if you want to allow commercial use, the BSD license (which I'm >significantly less familiar with). I think the current scheme works well. The problem with adding a license, is that we probably don't have the rights to add a lot of clauses. At least lots of the algorithms we use are not developed by ourselves. /* 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 ------------------------------ Date: Sat, 18 Sep 1999 22:45:11 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Mersenne: Re: G4: real or hype? On Sat, Sep 18, 1999 at 08:21:15AM +0200, Petri Holopainen wrote: >So this "128-bit 1 Gigaflops supercomputer" is just a load of >Apple marketing propaganda (yeah, Intel does this crap too, remember >"more vibrant colors" with MMX and "enhanced Internet experience" >with SSE...). Believe me, MMX can be quite useful, in some specialized situations (though perhaps not with everything...) I'm optimizing the reference MPEG-1/MPEG-2 decoder now, and it helps about 20% for just a few, very intense routines. /* 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 ------------------------------ Date: Sat, 18 Sep 1999 13:52:51 -0700 From: "John R Pierce" <[EMAIL PROTECTED]> Subject: Re: Mersenne: primes source > 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) ? Probably because of the hugely differing syntax and macro facilities. The assembler code was originally written with MASM on a Microsoft platform, if you feel up for converting it to `as` by all means, feel free. Make sure the resultant macro expansions are identical to the last byte of binary code. - -jrp _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 18 Sep 1999 16:54:49 -0400 From: George Woltman <[EMAIL PROTECTED]> Subject: Re: Mersenne: primes source Hi, At 03:01 PM 9/18/99 -0400, Darxus wrote: >I've just switched to the GIMPS. Welcome aboard. >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. >Also, the source seems to be released something like "feel free to use >this code to make the world a better place as you see fit", but doesn't >actually have a license. I would incourage you to release it under either >the GNU General Public License (http://www.gnu.org/copyleft/gpl.html), or >if you want to allow commercial use, the BSD license (which I'm >significantly less familiar with). I may look into changing this when the v19 sources are released. Regards, George _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 18 Sep 1999 23:47:28 +0200 (CEST) From: Henrik Olsen <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: primes source On Sat, 18 Sep 1999, Steinar H. Gunderson wrote: > On Sat, Sep 18, 1999 at 03:01:43PM -0400, Darxus wrote: > >I would incourage you to release it under either > >the GNU General Public License (http://www.gnu.org/copyleft/gpl.html), or > >if you want to allow commercial use, the BSD license (which I'm > >significantly less familiar with). > > I think the current scheme works well. The problem with adding a license, > is that we probably don't have the rights to add a lot of clauses. At least > lots of the algorithms we use are not developed by ourselves. 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. BTW, the gpl does not prevent commercial use. - -- Henrik Olsen, Dawn Solutions I/S URL=http://www.iaeste.dk/~henrik/ Flinx: Everybody wants to kidnap me. Oh well, I'll travel the galaxy and have boring adventures. (Pip the Flying Snake spits at something and kills it.) The Flinx of the Commonwealth Series, Book-A-Minute version _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 19 Sep 1999 00:24:13 +0200 From: "Lars Lindley" <[EMAIL PROTECTED]> Subject: Re: Mersenne: v19 manual workdodo.ini error. > Did you do this with prime95 running, or stopped? If prime95 was > running, it wouldn't notice the change in worktodo.ini until the next > iteration which is an exact multiple of 65536. Perhaps this explains > what you saw. > I did it with prime95 stopped. I have done this many times with v17 and v18 and I never had any problems with it... Regards /Lars _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 18 Sep 1999 19:03:15 -0600 From: "Mike Bean" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Celerons vs. Pentium II/III at large FFT lengths? > Accccckkkkkk! That was rather inexact wording. Let me try again...my > Celeron 400 based systems crunch exponents in the 384K FFT range at about > the same speed as George's PII-400 machine. However, at the 448K FFT size, > George's machine appears to be 20% or more faster than my Celeron 400s. > Could the 128K L2 cache of the Celeron chips (vs. the 512K L2 cache of the > PIIs) be the culprit? I think it is much more the bus speed/multipliers- tek = 4.5*100 cas = 5.5*83. | tek Celeron (Mendocino) 451.031641/451.031641 MHz 448.92/450.56 bms| | uptime 6:00pm up 8 days, 17:41, 0 users, load average: 2.00, 2.00, 2.00| | Iteration: 3850100 / 5515217 [69%]. Clocks: 81008907 = 0.180 sec. | | Iteration: 2357600 / 5511949 [42%]. Clocks: 81235328 = 0.181 sec. | | cas Celeron (Mendocino) 456.510316/456.510316 MHz 455.48/455.48 bms| | uptime 6:00pm up 17 days, 20:15, 0 users, load average: 2.00, 2.00, 2.0| | Iteration: 4084700 / 5505959 [74%]. Clocks: 97777645 = 0.217 sec. | | Iteration: 239600 / 5505919 [4%]. Clocks: 97636893 = 0.217 sec. | By the way is o/c frowned upon when running these tests? I got two errors back in early august (a sumout and a ERROR: ROUND OFF (0.5) > 0.40), two weeks after starting gimps, I adjusted the cooling and since then no reported errors. But overall am I wasting my time (an perhaps others) by running o/c'ed? _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 18 Sep 1999 20:12:17 -0600 From: "Mike Bean" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Celerons vs. Pentium II/III at large FFT lengths? > Accccckkkkkk! That was rather inexact wording. Let me try again...my > Celeron 400 based systems crunch exponents in the 384K FFT range at about > the same speed as George's PII-400 machine. However, at the 448K FFT size, > George's machine appears to be 20% or more faster than my Celeron 400s. > Could the 128K L2 cache of the Celeron chips (vs. the 512K L2 cache of the > PIIs) be the culprit? I'm sorry if my last message hit the list, both messages should just be ignored, this is just to correct the last one.. 448k, 100MHz bus cel 450 = 2.57 sec p3 = 2.49 sec less than 20% _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 18 Sep 1999 19:20:40 -0700 From: Eric Hahn <[EMAIL PROTECTED]> Subject: Mersenne: Factors Everywhere Ok, I've come up with this SWAHBI (like a SWAG, but an idea instead of a guess). What I'm looking for is the following two items for *all* Mersenne numbers 2^p-1 where p is prime and p>1: 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. I've pulled a couple of files off mersenne.org (FACTORS.ZIP and NOFACTOR.ZIP) as well as off Alex Kruppa's page. While the files appear complete as far as I can tell, they only cover the ranges of p between 11 - 9,999,991 and 33,219,281 - 35,999,993. They also don't cover *all* known factors! Any and all information on the ranges between 10M - 33.22M and >36M is greatly appreciated, as well as any known factors not listed in the files I've pulled. Eric Hahn _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 19 Sep 1999 00:03:00 -0700 (PDT) From: poke <[EMAIL PROTECTED]> Subject: 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 ------------------------------ Date: Sun, 19 Sep 1999 02:17:24 -0500 (CDT) From: Conrad Curry <[EMAIL PROTECTED]> Subject: 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 p>1: 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 ------------------------------ Date: Sun, 19 Sep 1999 00:40:48 -0700 From: Eric Hahn <[EMAIL PROTECTED]> Subject: 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 p>1: > > 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 p>100M, 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 ------------------------------ Date: Sun, 19 Sep 1999 03:02:34 -0500 (CDT) From: Conrad Curry <[EMAIL PROTECTED]> Subject: 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 oldrdf Relocatable 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 ------------------------------ Date: Sun, 19 Sep 1999 10:00:44 -0400 (EDT) From: Jason Stratos Papadopoulos <[EMAIL PROTECTED]> Subject: 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 ------------------------------ Date: Sun, 19 Sep 1999 18:47:46 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: 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 ------------------------------ Date: Sun, 19 Sep 1999 13:25:23 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: 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 $1000 US for any factor found of a number which ought to be prime (he provided a list). On that list was 2^(2^31-1)-1. I began searching for a factor of this number in mersfacgmp at around 12:10 Central standard time. I thought that mersfacgmp was malfunctioning, because it terminated too quickly, but I was wrong, it had found a factor! 295257526626031 divides 2^(2^31-1)-1, I have confirmed it in 3 different programs. Just to make sure that I haven't gone off the deep end, could Chris Caldwell confirm that he actually offered a prize for this number, and could the rest of you confirm that it is an actual factor? Also, Chris, I lost the sheet that had everyone's email address' at the conference, could you send me J.P. Selfridge's email address? Thank you, Lucas To guard against errors in transmitions the factor is 295257526626031 _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 19 Sep 1999 13:43:08 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: Mersenne: Re: Factor of 2^(2^31-1)-1 found ($ 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 ------------------------------ Date: Sun, 19 Sep 1999 13:53:58 -0400 From: "Chris Nash" <[EMAIL PROTECTED]> Subject: 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 ------------------------------ Date: Sun, 19 Sep 1999 11:23:50 -0700 From: "John R Pierce" <[EMAIL PROTECTED]> Subject: 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 ------------------------------ Date: Sun, 19 Sep 1999 22:12:28 +0200 (CEST) From: Henrik Olsen <[EMAIL PROTECTED]> Subject: 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 ------------------------------ Date: Sun, 19 Sep 1999 16:40:52 -0400 From: George Woltman <[EMAIL PROTECTED]> Subject: Mersenne: Re: Factor of 2^(2^31-1)-1 found ($) Hi, >On Sun, 19 Sep 1999, Lucas Wiman wrote: >> 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. Will Edgington maintains a list of known factors at http://www.garlic.com/~wedgingt/MMPstats.txt Regards, George _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 19 Sep 1999 16:58:54 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: Mersenne: Factor of M(M(31)) Ok, I should have researched a bit more. Many many people have informed me of will's site about M(M(p)) for various p's. I apreciate the link, but I have it now, I don't need any more of them. - -Lucas P.S. Warut, I hope you enjoy your money! :) _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 19 Sep 1999 16:03:30 -0500 (CDT) From: Chris Caldwell <[EMAIL PROTECTED]> Subject: 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 ------------------------------ Date: Sun, 19 Sep 1999 19:34:59 -0400 From: "Chris Nash" <[EMAIL PROTECTED]> Subject: 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 ------------------------------ Date: Sun, 19 Sep 1999 20:51:15 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: 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 ------------------------------ Date: Sun, 19 Sep 1999 21:23:47 -0400 From: "Chris Nash" <[EMAIL PROTECTED]> Subject: 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 k<2q+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 ------------------------------ End of Mersenne Digest V1 #628 ******************************
