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
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
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) (ATT 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
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
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
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
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
Re: Mersenne: Celerons vs. Pentium II/III at large FFT lengths?
Ackk! 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: 9645 = 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
Re: Mersenne: Celerons vs. Pentium II/III at large FFT lengths?
Ackk! 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
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 p1: 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
