QA (was re: Mersenne: Purpose of the self-test; also, aren't P4s fast!)
At 10:23 PM 5/15/2001 -, "Brian J. Beesley" <[EMAIL PROTECTED]> wrote: >On 14 May 2001, at 20:52, George Woltman wrote: >> >> >Is the self-test in fact just to check >> >that there's not something in the CPU which goes glitchy when running >> >flat-out SSE2 code for hours on end? >> >> Yes. The QA suite that Ken Kriesel and Brian Beesley worked on does a >> better job at testing edge conditions. Of course, they'll need to update that >> suite using the new limits. For the time being I would like to continue focussing our QA efforts on the general case, rather than P4's specific limits, since 1) there are relatively few P4's 2) we haven't finished QA testing in all run lengths with V19 / V20 (sign up now for a limited number of large exponents still available!) 3) the V19/20 QA now ongoing establishes "gold" residues over a huge range of exponents, against which other programs on other architectures can also be tested. >Actually most of the exponents in the test suite were chosen to >exercise code in a manner which is particularly hard on the "magic >numbers" involved in the collapsed DWT. Above is one of the methods of exponent selection. As George Woltman stated it: "Exponents that are close to a multiple of the FFT length." Other selection methods used to select full-LLtest exponents for QA were: 1) Already double-checked good numbers (or triple- or higher checked). Rerun to verify we can reproduce known-good results of previous versions or other code. 2) Duplicate the primality result for all known mersenne primes. (A special case of the above.) 3) The uppermost and lowest prime exponents within the determined limits for a given runlength. Always test limit cases. A little more than George suggested: "Those near the end of each range should be checked for excessive convolution error." 4) The prime exponent on either side of each integer power of two within the range supported by the program 5) Randomly selected prime exponents within the determined limits for a given runlength; typically one per higher runlength. The purpose of this set is to perhaps smoke out some case which we did not imagine. 6) We also tested a few composite exponents, just in case they behaved differently. 7) LLtests were except for #6, mostly done on exponents that had already run the gauntlet of trial factoring, p-1, and sometimes ecm. >Perhaps it would help us if George could indicate the approximate >limits for each run length when the SSE2 code is in use. Definitely. >But could I just point out that there is a _potential_ benefit in >running selftests using ridiculously small exponents for the run >length being tested. Normally the maximum permitted roundoff error is >0.4; this means that a roundoff error will only be detected as such >on one in every five occasions on which it occurs. If we use a small >exponent then we could reduce the roundoff error limit to 0.1 (or >maybe even less) and therefore detect a much larger proportion of any >roundoff errors which might occur. The fact that the residual checked >at the end of each self-test may still be correct does not prove that >a hardware glitch has not occurred, though gross errors will of >course cause the selftest to fail for this reason. If I recall correctly, this does not require "ridiculously" small exponents, since the convolution error falls off quickly away from our usual upper limit on exponent for a runlength. Convolution error varies with run length, exponent, and shift count. Running a case where we know the expected answer with high certainty: exponent, runlength, # of iterations, shiftcount? entered as qadata.txt 1279,40,1277,0, 1279,48,1277,0, 1279,56,1277,0, 1279,64,1277,0, output respectively Exp/iters: 1279/1277, res: 7653615CCA7AB4C0, maxerr: 4.00, maxdiff: 131072.0/529374.103214235 Exp/iters: 1279/1277, res: 5C21BA6CB463E665, maxerr: 0.50, maxdiff: 128.0/393.066381654 Exp/iters: 1279/1277, res: , maxerr: 0.157410, maxdiff: 1.0/2.342300785 Exp/iters: 1279/1277, res: , maxerr: 0.001817, maxdiff: 0.007812500/0.051145460 >Date: Fri, 07 May 1999 01:48:12 -0500 >To: George Woltman <[EMAIL PROTECTED]> >From: Ken Kriesel <[EMAIL PROTECTED]> >Subject: Re: more shift count variation qa results of 4423 > >At 09:07 AM 1999/05/06 -0400, you wrote: >>Hi Ken, >> >>At 12:29 AM 5/6/99 -0500, you wrote: >>>The cutoff at 4365 seems a little conservative; 4423 seems quite happy with >>>shift counts >>>that push it to maxerr 0.48. >> >>To me that indicates you could well run into a shift count that creates >>a maxerr > 0.50. > >You are correct; I did a baby perl script to generate big qa files, ran 4423 >through every shift count 0-999 and got: >980 of 0 residue >20 each of unique wrong residues. So the 2% probability of false negative is >not so good. Of course the program never state
Re: Mersenne: GIMPS accelerator?
Among others, I raised the question with George Woltman some time ago. I trust his judgment that his time is better spent elsewhere. However, I wonder if there might be some possibilities in trial factoring there. That would present the possibility of a factoring screensaver, and an FPU LLtest, running together on what is nominally a uniprocessor. Just speculation, Ken _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: games one can play with imaginary sheep
Paul Landon wrote: > Date: Tue, 15 May 2001 18:12:39 +0200 > From: Paul Landon <[EMAIL PROTECTED]> > Subject: Re: Mersenne: games one can play with genuine composites > [snip] > Cheers, > Paul Landon > > ps. Every train driver knows that Scottish sheep have > a maximum of 7 colours :-) > > ___ Generalization: It can be shown that the number of colours of Scottish sheep must be a Mersenne number. Therefore, the number must be 1, 3, or 7. _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: GIMPS accelerator?
> This question pops up every once in a while. A few years ago I looked > through a postscript manual wondering how difficult it would be to build a > postscript file that crunched RC5 keys when a printer tried to render it. postscript is essentially forth, after all. Trouble is, most postscript interpreters are pretty damn slow. > The latest bleeding edge graphics cards are programmable to a limited > degree (am I thinking of the ATI Radeon here?) but not nearly programmable > enough, I'm sure. NVIDIA's chips are semi programmable too, but a big hurdle is lack of documentation on the 3D rendering engine. That stuff is trade secret. I *do* suspect you could use the geometry engine (aka "Transformation Lighting and Projection") to do large numbers of fixed point 3x3 vector-matrix dot products with limited precision rather quickly. The question is, how useful would this be? The pipeline is probably such that you load one matrix and "transform" a large number of x,y,z vectors through it at a rather high speed. I'm not sure how useful this primitive would be in doing FFT operations. The newest Geforce3 chip also has both Pixel Shaders and Vertex Shaders which are each a SIMD programmable vector processors. The Pixel Shaders operate on every pixel and generate the actual RGB pixels while the Vertex Processors operate on the geometry and texture mapping coordinates of the 3D mesh... I don't know much about these, but pixels are only 8 bits per component so the pixel processors can't be very wide. I'm also not sure how fast you can get results OUT of the nvidia memory. Typically, these cards have 32-64MB of very high speed dedicated DDR SDRAM, but its optimized for the GPU to write into the memory, and the display refresh engine to read from it, I don't know how fast results could be read back into the host system -jrp _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: SUMOUT errors
I don't really know how much help this will be since I don't know your exact situation and am not a expert by any means, but here goes! First, the software modem may be a culprit. I have had problems with ones of the HSP variety. Most show up as 'HSP Micromodem56' or something very similar on your system. Most of these modems also use a chipset manufactured by PCTel. Fairly stable, but use a nice chunk of CPU time when online, and I have received errors when I am checking email and/or surfing the web while using this type of modem. I have no hard evidence to tie this modem to the errors, but all errors happened when I was using that modem or soon after (I hooked up a external modem just to see if the same would happen with it and I did not receive errors when using it). I have no idea if you have a modem similar to that one or not, but it may be the problem. Also, the electrical environment may be vastly different. I am assuming that where you had your computer was at school, and it is now at home. At my home, I have problems with various utility problems, and have been told by others that utility problems could cause such errors. I invested in a UPS with line conditioning to hopefully control some of those problems. Maybe one of these two things could be your problem.. I wish you the best of luck in finding and fixing the problem! - Jeramy _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: GIMPS accelerator?
John R Pierce wrote: > Virtually all GPU's in use today are fixed function hard wired graphics > accelerators. There's no way to use them for general purpose computational > use. Also, there's no APIs, and each chip vendor has a radically different > architecture. Too bad, the idea might also have given us an interesting screen saver as a side effect! :-) Cheers... Russ _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne Digest V1 #852
Mersenne Digest Tuesday, May 15 2001 Volume 01 : Number 852
--
Date: Mon, 14 May 2001 23:33:48 +0200
From: "Steinar H. Gunderson" <[EMAIL PROTECTED]>
Subject: Re: Overriding assigned exponent type (was Re: Mersenne: Re: 26 exponents)
On Mon, May 14, 2001 at 02:00:02PM -0700, Aaron Blosser wrote:
>I fear that many folks may not be aware of the list, or find
>that subscribing seems too hard (odd as that may sound to us experts :)
Or perhaps being set back by the description of an "in-depth discussion
about Mersenne primes"... ;-) When people start throwing the maths
around, I feel like I should take more maths soon :-P
Anyhow, no critique, but perhaps this _isn't_ a mailing list for the
general user. I personally like it, but the average SETI@Home `convert'
might not. Perhaps we could have a general `users' list instead?
/* 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: Tue, 15 May 2001 10:43:00 -0400
From: Nathan Russell <[EMAIL PROTECTED]>
Subject: Re: Overriding assigned exponent type (was Re: Mersenne: Re: 26 exponents)
On Mon, 14 May 2001 23:33:48 +0200, Steinar H. Gunderson wrote:
>On Mon, May 14, 2001 at 02:00:02PM -0700, Aaron Blosser wrote:
>>I fear that many folks may not be aware of the list, or find
>>that subscribing seems too hard (odd as that may sound to us experts :)
>
>Or perhaps being set back by the description of an "in-depth discussion
>about Mersenne primes"... ;-) When people start throwing the maths
>around, I feel like I should take more maths soon :-P
I'd tend to agree - the list is, at times, too in-depth for my
understanding, though it's lead me to do a fair amount of research on
my own. There are still discussions about CPU architecture, as well
as off-topic discussions about systems adminstration, that I don't
pretend to follow, but I've found that I've learned a lot reading
through those discussions.
As for a 'users' mailing list, I don't feel that that's necessary; if
'ordinary users' want to get on the list, they can simply read only
those threads that they understand and are interested in. The list
isn't so high-volume as to make that in any way prohibitive.
Nathan
_
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
--
Date: Tue, 15 May 2001 16:48:14 +0100
From: "Kevin Edge" <[EMAIL PROTECTED]>
Subject: Mersenne: Yeti at Home
You may be interested (briefly) in a new distributed computing
project that I have come across - Yeti at Home. Details at:
http://www.phobe.com/yeti/index.html
Kevin Edge
{:<)}
- ---
Kevin Edge - [EMAIL PROTECTED]
- ---
The opinions herein are my own and,
unless explicitly stated,
may not represent those of
Northgate Information Systems
_
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
--
Date: Tue, 15 May 2001 18:12:39 +0200
From: Paul Landon <[EMAIL PROTECTED]>
Subject: Re: Mersenne: games one can play with genuine composites
If a prime Q | M_C
then Order(2,Q) | C ;but not 1
Order(2,Q) | Q-1
F:=GCD(C,Q-1) != 1
F will either be C or one of it's divisors.
If Order(2,Q)==C then it has almost zero information
to tell us anything about the factors of C.
If C has 2 factors P0 & P1 then the product of factors
with Order == C is M_C/(M_P0.M_P1)
with Order == P1 is M_P1
Order == P0 is M_P0
(For more than 2 factors of C, Pofwo(C) is recursively
defined as M_C / all the pofwos of the divisors of C).
I would expect the probability that a factor of M_C
has these orders to be a non-decreasing function of these
products.
An approximation for the probabilities could be just the
ratio of these products.
Sadly for composites such as M727 which guesses have as
having a small number of factors and it is known that the
smallest factor is bigger than a decent bound, F will
equal M727 nearly all the time, and rarely will a factor
be found. There is also the rare case where the order of
Q <= M_C but F=M_C
The distribution of Mersenne Divisors is such that small
Q will tend to have a smaller order, and any Q<=2M_C
will not have order M_C.
If you are only searching for factors of M_C of the form
KC+1 then these will always have F=M_C and tell us nothing
about the factors of C. The only factors of M_C that help
with factoring C are those not of the form
Re: Mersenne: GIMPS accelerator?
On Tue, 15 May 2001, Gareth Randall wrote: > Also, any code would be very hardware specific, and may only work if the display was not displaying, say, a desktop. > > However, if someone could implement it, it could provide the *ultimate* in Mersenne related screen savers! What you'd see on the screen would be the actual calculations themselves taking place before your eyes, and with no overheads for displaying it either! This question pops up every once in a while. A few years ago I looked through a postscript manual wondering how difficult it would be to build a postscript file that crunched RC5 keys when a printer tried to render it. The latest bleeding edge graphics cards are programmable to a limited degree (am I thinking of the ATI Radeon here?) but not nearly programmable enough, I'm sure. Heck, at least these ideas have a better chance than the guys who want to crack the programming on kids' toys to make them crunch RC5 keys :) jasonp _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: SUMOUT errors
In the course of a single P-1 run, I've gotten 3 SUMOUT errors: [Tue May 15 08:20:24 2001] SUMOUT error occurred. [Tue May 15 12:04:41 2001] SUMOUT error occurred. [Tue May 15 20:05:15 2001] SUMOUT error occurred. In the past fifteen months with GIMPS, I had gotten only two errors. I can't help wondering if this could have something to do with a corrupt Win98 swapfile, since all of the errors occured during Stage 2; however, I would think that that would have caused far more errors. Additionally, I've only had one system I'll run a thorough Scandisk tonight. I don't know if CPU overheating might be a problem, since I just moved the machine home and it's about 70-75 Farenheit here during the day. The machine 'sounds' exactly the same, and since I have Asperger's Syndrome (a mild form of autism) I tend to trust my sense of hearing implicitely. That said, if there's a hardware problem of some sort, I'd want to have it checked out very promptly! The major changes in the past several days: 1. I am now using my modem rather than my ethernet card. 2. As said above, i'm home, and it's warmer (though the machine has operated in an environment that was warmer still this past August). Also, when I put my hand at the vent, it barely feels luke-warm - and it felt hot to the point of being uncomfortable before. 3. The machine was transported about 70 miles, and might have been somehow jolted - but appears to work fine. 4. All three errors occured during P-1 Stage 2, and I specifically remember that the machine was swapping fairly heavily at the time of the first and second errors (I had stopped back to check email). I'll reduce the allowed memory by 10 megs or so when this run is over. 5. I was using my software modem at those times - but not at the time of the third error, and I'd used it without trouble earlier this weekend, but not during heavy swapping. Any insight would be appreciated. I've never had stability problems before. I'll be more concerned if they continue when this P-1 run is over, at about midnight. Regards, Nathan _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Primestats perl script updated, (bug fix).
Hi All I've noticed that sometimes the topproducers table goes a bit strange, this causes the primestats script to output 2 Meg worth of error messages, not good if you run it in a cron job, and then the cron job backs up your inbox. So I've tracked the bug down and fixed it so now you only get 24 lines of error message when we have a problem with topproducers.shtml rather than 2 Megs worth. It's here: http://www.zeropps.uklinux.net/linstuff.html -- Cheers Steve email mailto:[EMAIL PROTECTED] %HAV-A-NICEDAY Error not enough coffee 0 pps. web http://www.zeropps.uklinux.net/ or http://start.at/zero-pps 1:35am up 103 days, 2:22, 2 users, load average: 1.03, 1.08, 1.11 _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: 26 exponents
At 10:23 PM 5/15/2001 +, Brian J. Beesley wrote: >Actually I think that there may be a perceptual problem with many new >users in that they may give up as soon as they realize that a "most >sense" assignment is going to take several weeks to complete. >Unfortunately there seems to be no easy way to fix this! How about a warning beforehand? Over 18,000 people have completed at least one assignment. Are the any figures for how many started, and then never finished? +-+ |Jud McCranie | | | | You'll never need more than 640 megs of memory. | +-+ _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Overriding assigned exponent type (was Re: Mersenne: Re: 26 exponents)
On Tue, May 15, 2001 at 10:23:33PM -, Brian J. Beesley wrote: >If you understand _nothing_ discussed on a mailing list, there's no >point in subscribing. Similarly if you understand _everything_. You >can always delete the messages which you consider beyond your >intellect, or beneath contempt. Personally I like the range we have >at present. Yes -- that is my opinion too. I skim quite a lot, though ;-) >Some of the deeper maths makes me go away & read up on the topic, & >occasionally I get a bit wiser as a result. Hmmm, I think I've learned quite a bit of maths just be skimming :-) It's surprising how much you can learn just by looking at a clueful calculation, even if you don't really understand the maths behind it. Now, just to print out my maths hand-in where one of the proofs utilizes (simple!) modular arithmetic, which I've learned... here. :-) (We haven't had it in school yet, but I suppose we will next year.) (If anybody wants to know, it's `prove that n^3 - n has 24 as a factor, for odd n' :-) ) /* 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: GIMPS accelerator?
We currently use the FPU (floating point unit) which most office software doesn't use. The GPU is hard coded for graphics and not really useful for anything else. --- Daran <[EMAIL PROTECTED]> wrote: > I know very little about computer architecture, so please feel free > to shoot > me down if what follow is complete nonsense. > > GIMPS clients use the spare capacity of the primary processing > resource within > any computer:- the CPU(s). But most modern PCs have another > component capable > of performing rapid and sophisticated calculations:- the GPU on the > graphics > accelerator. Is there any way that the GPU can be programmed to > perform GIMPS > processing when otherwise not in use? If this could be done, then it > would > have the effect of turning every client computer into an > multi-processor > system. > > Regards > > Daran G. > > > _ > Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm > Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers __ Do You Yahoo!? Yahoo! Auctions - buy the things you want at great prices http://auctions.yahoo.com/ _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Overriding assigned exponent type (was Re: Mersenne: Re: 26 exponents)
On 14 May 2001, at 23:33, Steinar H. Gunderson wrote: > Or perhaps being set back by the description of an "in-depth discussion > about Mersenne primes"... ;-) When people start throwing the maths > around, I feel like I should take more maths soon :-P > > Anyhow, no critique, but perhaps this _isn't_ a mailing list for the > general user. I personally like it, but the average SETI@Home `convert' > might not. Perhaps we could have a general `users' list instead? If you understand _nothing_ discussed on a mailing list, there's no point in subscribing. Similarly if you understand _everything_. You can always delete the messages which you consider beyond your intellect, or beneath contempt. Personally I like the range we have at present. Some of the deeper maths makes me go away & read up on the topic, & occasionally I get a bit wiser as a result. The usual problem with splitting a mailing list into "experts" & "novices" lists is that the "novices" list dies out for lack of any "expert" content. I don't think splitting this list would work unless the "novices" list was actively managed by a few of us who do have reasonable experience. 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: Purpose of the self-test; also, aren't P4s fast!
On 14 May 2001, at 20:52, George Woltman wrote: > > >Is the self-test in fact just to check > >that there's not something in the CPU which goes glitchy when running > >flat-out SSE2 code for hours on end? > > Yes. The QA suite that Ken Kriesel and Brian Beesley worked on does a > better job at testing edge conditions. Of course, they'll need to update that > suite using the new limits. > Presumably FPU code on processors other than the P4. But yes, it is and (to the best of my knowledge) always has been a hardware test rather than a test of the software, at any rate once the software is in the hands of users. Actually most of the exponents in the test suite were chosen to exercise code in a manner which is particularly hard on the "magic numbers" involved in the collapsed DWT. I'm sure we can find some more exponents & extend the test suite so that more candidates are available in the appropriate range for each FFT run length. Probably this was getting overdue anyway, given the increasing performance of available processors. Perhaps it would help us if George could indicate the approximate limits for each run length when the SSE2 code is in use. But could I just point out that there is a _potential_ benefit in running selftests using ridiculously small exponents for the run length being tested. Normally the maximum permitted roundoff error is 0.4; this means that a roundoff error will only be detected as such on one in every five occasions on which it occurs. If we use a small exponent then we could reduce the roundoff error limit to 0.1 (or maybe even less) and therefore detect a much larger proportion of any roundoff errors which might occur. The fact that the residual checked at the end of each self-test may still be correct does not prove that a hardware glitch has not occurred, though gross errors will of course cause the selftest to fail for this reason. If this idea is developed, it's important to be aware that using too small an exponent for a particular run length can invalidate the "subtract two" coding in the LL test. I think the lower limit is three bits per element, though this may depend to some extent on the exact way in which the code is implemented. 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: 26 exponents
On 14 May 2001, at 21:56, Nathan Russell wrote: > otherwise, you might > have someone using a 486 suddenly realize that their computer was > doing a first-time check that would take over a year, get frustrated, > and give up. A first-time check on a 10M exponent would take _several_ years on a 486! Actually I think that there may be a perceptual problem with many new users in that they may give up as soon as they realize that a "most sense" assignment is going to take several weeks to complete. Unfortunately there seems to be no easy way to fix this! > > >There is also a theoretical difference between those exponents > >congruent to 1 modulo 4 and those congruent to 3 modulo 4. However I > >believe that this is due to the fact that one of these groups has a > >larger probability of having a small factor; thus this irregularity > >is removed by the time that LL testing begins. > > I think I read something similiar. Might it relate to whether the > first potential factor itself is prime, specifically whether it is > divisible by 3? I can't do the arithmetic in my head, but I have a > hunch... Um. 2p+1 = 3 mod 4 irrespective of whether p = 1 mod 4 or p = 3 mod 4 However for "large" p there doesn't seem to be any link to divisibility of 2p+1 by 3, or any other "small" prime. The obvious bias against 3 mod 4 exponents is that those which are Sophie-Germain primes are guaranteed to be divisible by 2p+1. We can also examine 2kp+1 mod 8, which must be 1 or 7 if it is a candidate factor of M(p). When p = 1 mod 4, p = 1 mod 8 or p = 5 mod 8, so 2p = 2 mod 8, therefore: 2p+1 = 3 mod 8, so can't be a factor 4p+1 = 5 mod 8, so can't be a factor 6p+1 = 7 mod 8, so might be a factor 8p+1 = 1 mod 8, so might be a factor ... so the values of k which checking are 3, 4, 7, 8, 11, 12, ... When p = 3 mod 4, p = 3 mod 8 or p = 7 mod 8, so 2p = 6 mod 8, therefore 2p+1 = 7 mod 8, so might be a factor 4p+1 = 5 mod 8, so can't be a factor 6p+1 = 3 mod 8, so can't be a factor 8p+1 = 1 mod 8, so might be a factor ... so the values of k which need checking are 1, 4, 5, 8, 9, 12, ... The multiples of 4 are common to both series, but the other possible k values are smaller in the p = 3 mod 4 series than those in the p = 1 mod 4 series. And, other things being equal, smaller k values are in general more likely to be provide a factor than larger ones. However, trial factoring to k >> 10^6 surely reduces the difference to a miniscule amount. > Perhaps clicking the 'give me the work that makes the most sense' box > should immediately set the appearance of the others to the work that > will be chosen, rather than simply graying them out. Agreed. 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: GIMPS accelerator?
Daran, This is an interesting piece of lateral thinking that deserves to go further than I think it actually does. Essentially, I'm not sure how the operations that a graphics card can provide, such as line drawing, texture overlaying, raytraced light effects etc, could be made to implement a LL test or FFT etc which would require things like bit tests, conditioning branches and loops etc. Conceivably additions could be done by superimposing textures and reading back the resulting frame buffer, but these wouldn't be 64-bit precision additions! Maybe some form of matrix multiplication could be done by rotating textures before superimposing? However, I think the resulting calculation efficiency would be very poor, and may never achieve useful precision. Also, any code would be very hardware specific, and may only work if the display was not displaying, say, a desktop. However, if someone could implement it, it could provide the *ultimate* in Mersenne related screen savers! What you'd see on the screen would be the actual calculations themselves taking place before your eyes, and with no overheads for displaying it either! Yours, === Gareth Randall === Daran wrote: > > I know very little about computer architecture, so please feel free to shoot > me down if what follow is complete nonsense. > > GIMPS clients use the spare capacity of the primary processing resource within > any computer:- the CPU(s). But most modern PCs have another component capable > of performing rapid and sophisticated calculations:- the GPU on the graphics > accelerator. Is there any way that the GPU can be programmed to perform GIMPS > processing when otherwise not in use? If this could be done, then it would > have the effect of turning every client computer into an multi-processor > system. _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: 26 exponents
On Tue, May 15, 2001 at 04:48:19PM +0100, Daran wrote: >BTW what happens now when a first-time check, (or for that matter, if a >double-check) discovers a new prime. Surely this is checked immediately on >the fastest machine available to the project, and not left to the vagaries of >random allocation? It is run on a different architecture, with different software. The three first were (as far as I know) tested on Crays, while the 4th (M38 (we think)) was tested on an Alpha machine with mlucas, as far as I remember. The idea is to completely eliminate any possibility of a persistent program or hardware bug :-) /* 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: GIMPS accelerator?
--- Daran <[EMAIL PROTECTED]> wrote: > I know very little about computer architecture, so please feel free > to shoot > me down if what follow is complete nonsense. > > GIMPS clients use the spare capacity of the primary processing > resource within > any computer:- the CPU(s). But most modern PCs have another > component capable > of performing rapid and sophisticated calculations:- the GPU on the > graphics > accelerator. Is there any way that the GPU can be programmed to > perform GIMPS > processing when otherwise not in use? If this could be done, then it > would > have the effect of turning every client computer into an > multi-processor > system. > > Regards > > Daran G. > > > _ > Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm > Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers __ Do You Yahoo!? Yahoo! Auctions - buy the things you want at great prices http://auctions.yahoo.com/ _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: P4 executable
Hi all, I've uploaded a version that fixes 2 bugs in the new P4 prime95. 1) Trial factoring was broken. In switching to MASM 6.15, an assembler bug caused the factoring code to blow up. 2) I restored a FPU init instruction that I accidentally deleted. This caused the excessive round-off errors when running the old FFT code. Again, *FOR P4 USERS ONLY* the fixed version is at ftp://mersenne.org/gimps/p95v21a.zip Have fun, George _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: 26 exponents
At 04:34 PM 5/15/2001 +0100, Daran wrote: >Are there any exponents below #38 that have never been assigned? Not as far as I know, but there are over 20 that haven't had the first LL test completed. But they should have all been assigned at least 24 months ago. ++ | Jud McCranie | || | former temporary part-time adjunct | | instructor of a minor university | ++ _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: GIMPS accelerator?
> I know very little about computer architecture, so please feel free to shoot > me down if what follow is complete nonsense. > > GIMPS clients use the spare capacity of the primary processing resource within > any computer:- the CPU(s). But most modern PCs have another component capable > of performing rapid and sophisticated calculations:- the GPU on the graphics > accelerator. Is there any way that the GPU can be programmed to perform GIMPS > processing when otherwise not in use? If this could be done, then it would > have the effect of turning every client computer into an multi-processor > system. Virtually all GPU's in use today are fixed function hard wired graphics accelerators. There's no way to use them for general purpose computational use. Also, there's no APIs, and each chip vendor has a radically different architecture. -jrp _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: ECM Question...
I think I know the answer to this question, but am asking it... just to make sure... According to ECMNet, to find factors of up to 25 digits, the optimal B1 is 50,000 with 300 expected curves... and to find factors of up to 30 digits the optimal B1 is 250,000 with 700 expected curves... If a person runs an ECM test using a B1 of 250,000 with 700 curves (for up to 30 digits), will they also find any factors that they would have found if they had used a B1 of 50,000 with 300 curves (for up to 25 digits) ?!? Eric I'm presuming the answer is yes... and it works the same for each level... (1,000,000 with 1800 expected curves for up to 35 digits, etc.)... _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: missing exponents?
-Original Message- From: Nathan Russell <[EMAIL PROTECTED]> To: [EMAIL PROTECTED] <[EMAIL PROTECTED]> Date: 15 May 2001 03:25 Subject: Re: Mersenne: missing exponents? >I have version 20.6.1 - and the web page reads that all versions were >last updated June 15 2000. Something odd is going on... That's the version I'm running. Has there been an update since last June that I don't know about? >Nathan Daran G. _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: GIMPS accelerator?
I know very little about computer architecture, so please feel free to shoot me down if what follow is complete nonsense. GIMPS clients use the spare capacity of the primary processing resource within any computer:- the CPU(s). But most modern PCs have another component capable of performing rapid and sophisticated calculations:- the GPU on the graphics accelerator. Is there any way that the GPU can be programmed to perform GIMPS processing when otherwise not in use? If this could be done, then it would have the effect of turning every client computer into an multi-processor system. Regards Daran G. _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: 26 exponents
-Original Message- From: Jud McCranie <[EMAIL PROTECTED]> To: [EMAIL PROTECTED] <[EMAIL PROTECTED]> Date: 15 May 2001 04:34 Subject: Re: Mersenne: Re: 26 exponents >At 09:44 PM 5/14/2001 -0400, Nathan Russell wrote: >They would still be contributing towards milestones. If there are >exponents below a milestone that never have been assigned, they would get >them. Are there any exponents below #38 that have never been assigned? [...] >But there could be one smaller than what now seems to be #38, because there >are exponents in that range that haven't had even 1 LL. I'm not adept at the number theory, but presumably these are more likely to be prime for no other reason than because they are relatively small, and the density of Mersenne primes decreases with size. >| Jud McCranie | Daran G. _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: 26 exponents
-Original Message- From: Steve <[EMAIL PROTECTED]> To: [EMAIL PROTECTED] <[EMAIL PROTECTED]> Date: 14 May 2001 07:59 Subject: Re: Mersenne: Re: 26 exponents >That _might_ be a good idea, except in the eventual situation where both >participants return results indicating their number is indeed prime. Whoever >had the slightly slower machine will not be very happy! That gets my vote for understatement-of-the-year. :-) BTW what happens now when a first-time check, (or for that matter, if a double-check) discovers a new prime. Surely this is checked immediately on the fastest machine available to the project, and not left to the vagaries of random allocation? >Steve Harris Daran G. _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: 26 exponents
-Original Message- From: Nathan Russell <[EMAIL PROTECTED]> To: [EMAIL PROTECTED] <[EMAIL PROTECTED]> Date: 13 May 2001 02:58 Subject: Re: Mersenne: Re: 26 exponents >On Sat, 12 May 2001 18:21:17 -0400, Jud McCranie wrote: >There would still be a distinction drawn between 'new' and >'experienced' users, and I think drawing any such distinction would >make new users feel less valued - and quite possibly lead them to join >one of the other fairly large projects, all of which are completely, >or nearly completely, automated. Why should there be any less automation if multiply expired exponents are only awarded to fast machines with a track record of reliability? Alternatively, since nobody seems to find it objectionable, why not take these exponents off the primmest server, and offer them to list subscribers only? >Nathan Daran G. _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: 26 exponents
-Original Message- From: Nathan Russell <[EMAIL PROTECTED]> To: [EMAIL PROTECTED] <[EMAIL PROTECTED]> Date: 14 May 2001 14:31 Subject: Re: Mersenne: Re: 26 exponents >On Mon, 14 May 2001 00:20:47 +0100, Daran wrote: > >>As someone currently running a legacy machine, (It's taking 4-5 months to run >>double-checks in the range under consideration,) I have some thoughts on this. >> >>First of all, as Jud notes, the 'elitism' is already there, in that different >>machines get treated differently in the assignments that they are given. It >>also lies at the heart of the 'Top producer' chart. > >Every distributed computing project larger than a few dozen members >has such a chart. It would be difficult to keep people interested >without one. I know that I don't feel less a part of the project >because my placing is above 4,000. I daren't look at my placing, but I'm pretty sure I'm going backwards. :-) >>Even readers of this list >>get opportunities to acquire exponents or prebeta-test software, etc., that >>are not available to the unwashed masses. > >Very true. Of course, George can hardly contact all several thousand >participants when such an opportunity happens. As I said, the intention is not to criticise current practice, but to point at that there is already differential treatment between participants, and that it really isn't something to worry about, IMO. [...] >>If I choose to specify what kind of work I want, I >>still expect the be given the work that "makes most sense" within that >>category. I certainly would not expect to be given work that would delay a >>milestone, given the limitations of my machine. > >This might be a reasonable change in PrimeNet. Personally, I don't >think milestones should be a focus of the project, but it is nice when >a new one appears on the page. True. Similarly top producer ranking isn't a focus of the project, but it's nice (or not nice, in my case) to see how well you're doing. [...] >I still think that this is very debatable. There should not be a >certain /assignment type/ reserved for 'veterans', but it may be >reasonable to, e.g., only give triple-checks to accounts that request >double-checks, and have returned more than a certain number of >results. In what way is that not reserving an assignment type - triple-checks - to veterans? >>People need to be informed about >>departures from documented practice. > >Are you suggesting that, every time George offers exponents to the >members of this mailing list, he should send out a newsletter to every >participant - guaranteeing hundreds or thousands of replies for him to >deal with? I think there may be no good solution to this. No, of course not. I meant changes in practise that affect /them/. For example the suggestion that an exponent be assigned to two people simultaneously, with the first one back counting as the primary test, and the second as the double-check. If I asked for a first-time check (or if I thought I had been given one), then I should not be happy if I found out later that someone else had gotten there first.. >Nathan Daran G. _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: 26 exponents
-Original Message- From: Nathan Russell <[EMAIL PROTECTED]> To: Brian J. Beesley <[EMAIL PROTECTED]>; [EMAIL PROTECTED] <[EMAIL PROTECTED]> Date: 15 May 2001 03:26 Subject: Re: Mersenne: Re: 26 exponents >Agreed. Membership to the list indicates a slightly-more-than-casual >interest in the project, specifically a willingness to sift through a >few dozen messages per month in order to learn more about the project. >That interest might well also be a sign of someone who is more likely >to faithfully complete 'special' assignments in a relatively timely >fashion. I'm sure it is. My intention wasn't to criticise the practice. It just seems absurd to me to worry about 'elitism' in the choice of actual exponent assigned, which the user isn't going to be aware of anyway, and then to be content with the 'elitism' in the 'most sense' choice of test type, or in the additional opportunities afforded to list members. I put 'elitism' into quotes because I don't agree that it is elitism at all. >Nathan Russell Daran G. _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: 26 exponents
-Original Message- From: Jud McCranie <[EMAIL PROTECTED]> To: [EMAIL PROTECTED] <[EMAIL PROTECTED]> Date: 15 May 2001 04:52 Subject: Re: Mersenne: Re: 26 exponents >Well, how about this - new users can get an exponent that has been >abandoned several times, but they must check in at least once a month to >report the percentage done and expected completion date to show that they >are making reasonable progress. It could even be automatic. Or maybe check >in at 1 month, 2 months after that, and then every three months? Or is >that too elitist too? No, It's just too complicated. Regards Daran _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: games one can play with genuine composites
If a prime Q | M_C then Order(2,Q) | C ;but not 1 Order(2,Q) | Q-1 F:=GCD(C,Q-1) != 1 F will either be C or one of it's divisors. If Order(2,Q)==C then it has almost zero information to tell us anything about the factors of C. If C has 2 factors P0 & P1 then the product of factors with Order == C is M_C/(M_P0.M_P1) with Order == P1 is M_P1 Order == P0 is M_P0 (For more than 2 factors of C, Pofwo(C) is recursively defined as M_C / all the pofwos of the divisors of C). I would expect the probability that a factor of M_C has these orders to be a non-decreasing function of these products. An approximation for the probabilities could be just the ratio of these products. Sadly for composites such as M727 which guesses have as having a small number of factors and it is known that the smallest factor is bigger than a decent bound, F will equal M727 nearly all the time, and rarely will a factor be found. There is also the rare case where the order of Q <= M_C but F=M_C The distribution of Mersenne Divisors is such that small Q will tend to have a smaller order, and any Q<=2M_C will not have order M_C. If you are only searching for factors of M_C of the form KC+1 then these will always have F=M_C and tell us nothing about the factors of C. The only factors of M_C that help with factoring C are those not of the form KC+1. Stating the obvious, M_C is exponentially bigger than C and even a trial divison of M_C using exponentiation will take longer than meaningful operations on C. For example a division of M_M727 is not practical, but if a factor of M_C is found it is worth doing one GCD. So an approximate heuristic that anyone can better by not using a geometric mean or using knowledge of the distribution of Mersenne Divisors, is that for C having 2 factors, the probability of Q | M_C helping with factoring C is approx:- M_P0 + M_P1 --- M_C+ M_P0 + M_P1 - M_P0.M_P1 or not a lot! Cheers, Paul Landon ps. Every train driver knows that Scottish sheep have a maximum of 7 colours :-) _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Yeti at Home
You may be interested (briefly) in a new distributed computing
project that I have come across - Yeti at Home. Details at:
http://www.phobe.com/yeti/index.html
Kevin Edge
{:<)}
---
Kevin Edge - [EMAIL PROTECTED]
---
The opinions herein are my own and,
unless explicitly stated,
may not represent those of
Northgate Information Systems
_
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Overriding assigned exponent type (was Re: Mersenne: Re: 26 exponents)
On Mon, 14 May 2001 23:33:48 +0200, Steinar H. Gunderson wrote: >On Mon, May 14, 2001 at 02:00:02PM -0700, Aaron Blosser wrote: >>I fear that many folks may not be aware of the list, or find >>that subscribing seems too hard (odd as that may sound to us experts :) > >Or perhaps being set back by the description of an "in-depth discussion >about Mersenne primes"... ;-) When people start throwing the maths >around, I feel like I should take more maths soon :-P I'd tend to agree - the list is, at times, too in-depth for my understanding, though it's lead me to do a fair amount of research on my own. There are still discussions about CPU architecture, as well as off-topic discussions about systems adminstration, that I don't pretend to follow, but I've found that I've learned a lot reading through those discussions. As for a 'users' mailing list, I don't feel that that's necessary; if 'ordinary users' want to get on the list, they can simply read only those threads that they understand and are interested in. The list isn't so high-volume as to make that in any way prohibitive. Nathan _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Overriding assigned exponent type (was Re: Mersenne: Re: 26 exponents)
On Mon, May 14, 2001 at 02:00:02PM -0700, Aaron Blosser wrote: >I fear that many folks may not be aware of the list, or find >that subscribing seems too hard (odd as that may sound to us experts :) Or perhaps being set back by the description of an "in-depth discussion about Mersenne primes"... ;-) When people start throwing the maths around, I feel like I should take more maths soon :-P Anyhow, no critique, but perhaps this _isn't_ a mailing list for the general user. I personally like it, but the average SETI@Home `convert' might not. Perhaps we could have a general `users' list instead? /* 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
