Re: Mersenne: Reliability of prime95 vs. PRP
On 5 Feb 2001, at 22:06, George Woltman wrote: Maybe it would be useful to show a 64-bit residue after completion of the probable prime test? True, but no one has volunteered to keep a central list of residues, much less organize a rigorous search of Proth candidates. Is this really neccessary? I'd be more interested in what happens to those candidates which pass PRP and go on to Proth, or PrimeGen. If Proth finds "not prime" it doesn't tell you anything else. There is a chance that something glitched. Presumably also the residue will depend on which base you use for the Proth test, I'm not sure the program always makes the same choice. Please excuse my ignorance. However I certainly agree that the search needs to be organized better before anyone starts worrying about possibly missing ~1% of the primes in a "searched" range. I messed around with Proth a couple of years ago, registered some ranges (the mechanism doesn't seem to have changed since) and found 4 primes over 20,000 digits in a couple of P100 CPU months - these were just about "top 500" at the time - of which 2 turned out to be rediscoveries from someone else working on the same ranges without bothering to register them. Not very encouraging :( When Proth does find a prime, it verifies it by a second test using the same program on the same system but using a different base. This doesn't "feel" as good as GIMPS/PrimeNet's independent double- checking mechanism. Incidentally, am I missing something? The Fermat test for pseudoprimality (which is equivalent to a Proth test for true primality, given a suitable candidate number and a suitable choice of base) takes as long to run as a LL test on a number of the same size. So, what test is PRP running? Obviously there's no point in running Fermat's test with base 2 for Mersenne numbers, but I find it somewhat less obvious that Fermat's test with base 2 would eliminate a useful proportion of Proth candidates. If PRP is doing something else, and runs significantly faster than Fermat's test, is there any point in using it to pre-filter Mersenne candidates??? For now, it looks to me like GIMPS is the most reliable way of looking for primes. Does anyone on the list have a view on this? Both are quite reliable methods for finding primes. One is good at finding good sized primes, the other good at finding record primes. BTW, the Proth program and OpenPFGW program could be used to find world-record primes. They are less than half as efficient as prime95 - but you get to test numbers that are much smaller than the M1200 currently being assigned by Primenet. Before June 1999 there was some discussion about using Proth to find a million-digit prime for the EFF prize. Things may have changed since, but I seem to remember that a new version of Proth was rushed through to give it this capability, and even then the code used was becoming distinctly marginal when testing numbers of that size. The (semi-)organized use of Proth has concentrated on smaller numbers; the biggest would be candidate Cullen prime numbers (p.2^p+1) with p around 1 million, i.e. the order of 300,000 digits. Robert's suggestion of using old, slow Pentium systems would make very little sense if you were wanting to use Proth or OpenPFGW to look for prime numbers around 2^7,000,000. The run times would be just as long as LL test assignments using Prime95. 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: [screen saver]
There's a rather good freeware screen saver written by Gianpaolo Bottin called GPhotoShow. It's just a slide show with transitions and provides a *lot* of free CPU time in between the pictures -- I run it along with Prime95 on this computer (450 pII) and there is no noticeable slowdown in either program on any priority setting. This could suffice unless a person wanted a GIMPS display integrated into the screen saver, though I'm not sure at all what there would be to display. Just throwing this out to the list. :) ~ Levi http://www.bottin.com/gpshow.htm - Original Message - From: "Steve" [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, February 05, 2001 10:38 PM Subject: Re: Mersenne: Re: idea for a new prime95 version Excellent idea, Russ. I was discussing with Like Welsh the problem of people attached to their killer screensavers, and as he pointed out: "But maybe they'd watch pic of their kids/dog/vacation instead? The *particular* screensaver I was thinking of was the Photo Slide Show variety. Slap an image on the screen, wait 15 seconds, fade out, display another. Lots of free CPU time between pics." Certainly it won't work for everybody, but I'm sure there would be a lot of takers. Now, anybody know how to write such a thing? Could be released with the prime95/NT software or as a seperate item to be downloaded from the same site. Steve Harris _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne Digest V1 #813
Mersenne Digest Tuesday, February 6 2001 Volume 01 : Number 813 -- Date: Sat, 3 Feb 2001 23:16:56 -0800 From: "Stephan T. Lavavej" [EMAIL PROTECTED] Subject: Mersenne: Re: Mersenne Digest V1 #812 What about some of the new gaming platforms. I think some have computing capabilities equivalent to P133s and they have modem hookups. However, I'm not sure how feasible/worthwhile it would be to write progamrs to do this. Better yet, the Xbox. It will actually have a PIII-733 inside it, AND a hard drive, and a built-in broadband connection. All that would be required is the ability to run arbitrary code from the hard drive, and poof, you have something like a million potential boxes on which to run Prime95. Stephan T. Lavavej http://quote.cjb.net _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers -- Date: Sun, 4 Feb 2001 01:50:18 -0600 From: "Steve" [EMAIL PROTECTED] Subject: Re: Mersenne: idea for a new prime95 version "Alexander Kruppa" wrote: The screen-saver idea is important for another reason. I asked several coworkers and secretaries to let Prime95 (NTprime, actually) run on their PCs and they agreed, but they were less than happy when I asked them to change the pretty 3-d screen savers for something that lets NTprime have more cpu power. With the selection Microsoft offers right now, that means "Blank Screen" or "Marquee" - neither is extremely exciting to watch. Before long, most of them went back to the old screen savers and NTprime slowed down to a halt. "...slowed down to a halt" is no exaggeration. I've seen screensavers slow it down to more than 7 seconds per iteration at 800+ MHz. I have it running on some PCs where the user has the screensaver set to start after 5 minutes then sets the power management so the monitor turns off after 10 or 15 minutes... and what really bothers me is that the screensaver continues to run even with the monitor off. (Is there some way to prevent that which I don't know about?) One idiot even had her settings such that the screensaver didn't start until _after_ the monitor went off. There are so many screensavers available now that one can be found to match any personality, and I have found it impossible to get people to let go of one they really like. So I don't believe Brian's idea will do very much good; but then every little bit helps. Steve Harris [EMAIL PROTECTED] _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers -- Date: Sun, 04 Feb 2001 00:16:03 -0800 From: Luke Welsh [EMAIL PROTECTED] Subject: Re: Mersenne: idea for a new prime95 version At 01:50 AM 2/4/01 -0600, Steve wrote: There are so many screensavers available now that one can be found to match any personality, Why not identify a couple of existing screensavers that could be "compatible" with Prime95 and then approach the author(s). ask them to make a verion that includes George's stuff? - --Luke _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers -- Date: Sun, 4 Feb 2001 14:36:05 - From: "Brian J. Beesley" [EMAIL PROTECTED] Subject: Re: Mersenne: idea for a new prime95 version, QA, primenet etc On 3 Feb 2001, at 17:03, Jeff Woods wrote: With increasing exponent size (and therefore run time), I'd like to see PrimeNet evolve to track intermediate residues also to be able to coordinate parallel LL testing double-checking, so that runs which are going wrong can be stopped for investigation without having to be run through to the end. I think this is an EXCELLENT idea, but remember that the "s" values (i.e. the intermediate residue/modulus) for such numbers is quite simply enormous. One couldn't (and shouldn't) check the entire intermediate value, but merely the last "x" bits, where "x" is enough to be reasonably certain that a match isn't random chance -- say, the final 1024 bits. 64 bits is enough to be pretty confident! We need a recovery procedure anyway, to cope with any systematic bugs which may exist. PrimeNet would thus also have to carefully assign the exponents to similar machines with similar runtimes and performance, as it would do little good to assign the primary test to an Athlon-800 and the "real-time" double-check to a much slower machine, as the Athlon would quickly outpace the second check. If a discrepancy was found in a real-time double-check, a ternary run on a different machine could
Re: Mersenne: [screen saver]
Dear All, Let's face it, why should people who are primarily interested in mathematical computation divert their time to writing rather unimpressive screen savers? There are already plenty of programmers out there who can do that job better! So... Simply have an online list of "recommended" / "approved" / "suitable" screensavers. No-one has to write anything new. We just test those which already exist, and analyse what resource demands they make in terms of CPU usage, RAM access, process image size etc. Such a list can then allow contributors to select their preferred screensaver, and avoids introducing extra development complications. Yours, === Gareth Randall === _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: GIMPS SETI@Home Popularity
Date: Sat, 03 Feb 2001 20:05:45 -0500 From: "Joshua Zelinsky" [EMAIL PROTECTED] Subject: Mersenne: Misc Stuff. A few minor comments. *snip* 5. One reason SETI is more popular is that they seem to have good media relations. Even if we could get a small mention of GIMPS in some non-math publication, the effect could be enormous. The Science Section of the NYT would be really amazing. Any thoughts? Long ago I got some local media coverage: http://getty.net/gimps/polec/ but I did not see any enormous GIMPS participation leaps locally I would have to agree that SETI is definitely more popular because it is "sexy". -Marc Marc Getty [EMAIL PROTECTED] http://www.temple.edu/dentistry/di/ Department of Dental Informatics, Temple University School of Dentistry Phone: 215-707-8192Fax: 215-707-2208 New Dental School Room 311 _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: [screen saver]
Levi, does that GPhotoShow allow someone to use their own pictures? That's exactly what I was talking about. If so please let me know where I can get it. Some of you seem to misunderstand what I am getting at. I'm sure most serious contributors don't want a screensaver (I detest them), but in a situation where a friend or co-worker lets you install Prime95 on their PC but just HAS to have one (especially a really slow one), I would like to give them an option which: #1 - is Prime95 friendly and #2 - is easy to convince them to use. The "personal photo slide show" fits both of those criteria wonderfully. I know there are a lot of freeware screensavers available, and I know a lot of them don't hog cpu cycles too badly, but if this is the best one for both reasons above then we should make it available to those who can use it. I am losing literally hundreds of P90 hours a day to screensavers but I can't tell my friends not to run them because they'll just tell me to remove Prime95 from their PC and that's even worse! You should all know by now that there are a lot of people running Prime95 who couldn't care less about it, but will let it run if someone asks. OK so I'm anal-retentive about optimization. Sorry :-) Steve -Original Message- From: Levi Broderick [EMAIL PROTECTED] To: [EMAIL PROTECTED] [EMAIL PROTECTED] Date: Tuesday, February 06, 2001 3:45 PM Subject: Re: Mersenne: [screen saver] There's a rather good freeware screen saver written by Gianpaolo Bottin called GPhotoShow. It's just a slide show with transitions and provides a *lot* of free CPU time in between the pictures -- I run it along with Prime95 on this computer (450 pII) and there is no noticeable slowdown in either program on any priority setting. This could suffice unless a person wanted a GIMPS display integrated into the screen saver, though I'm not sure at all what there would be to display. Just throwing this out to the list. :) ~ Levi http://www.bottin.com/gpshow.htm - Original Message - From: "Steve" [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, February 05, 2001 10:38 PM Subject: Re: Mersenne: Re: idea for a new prime95 version Excellent idea, Russ. I was discussing with Like Welsh the problem of people attached to their killer screensavers, and as he pointed out: "But maybe they'd watch pic of their kids/dog/vacation instead? The *particular* screensaver I was thinking of was the Photo Slide Show variety. Slap an image on the screen, wait 15 seconds, fade out, display another. Lots of free CPU time between pics." Certainly it won't work for everybody, but I'm sure there would be a lot of takers. Now, anybody know how to write such a thing? Could be released with the prime95/NT software or as a seperate item to be downloaded from the same site. Steve Harris _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: Mersenne Digest V1 #813
For now, it looks to me like GIMPS is the most reliable way of looking for primes. Does anyone on the list have a view on this? Both are quite reliable methods for finding primes. One is good at finding good sized primes, the other good at finding record primes. BTW, the Proth program and OpenPFGW program could be used to find world-record primes. They are less than half as efficient as prime95 - but you get to test numbers that are much smaller than the M1200 currently being assigned by Primenet. The best candidates are not the numbers of the form k.2^n+/-1 but the numbers of the form b^(2^n)+1 (Generalized Fermat Numbers). Like for Mersenne numbers, we can use a DWT which computes directly x^2 (mod b^N+1). Then if we select carefully the ranges for b, the computation time to test the probable primality of a GFN is the same than the test of a Mersenne number with the Lucas-Lehmer test. The current version of Proth.exe implements this algorithm: I ran a bench on a PIII 600 and it is as fast as Prime95 up to about 10^6 digits and is about 30% slower for 12,000,000 digits. An operation with a GFN of 3,000,000 digits is about 4 times faster than an operation with a Mersenne number of 12,000,000 digits and the number of operations to compute to test a number 4 times smaller is divided by 4. And smaller is the number, larger is the probability to find a prime. Yves _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Embedding Prime95 inside a ScreenSaver
I've been having offline discussion with Steve. Some people (I know one admin) don't want Prime95 to run unless the machine is *really* idle. These people like a screensaver to run when, in their minds, the PC is idle. And there is no way to change their minds. The machines are theirs. Period. End Of Discussion. A version of Prime95 could be embedded/hidden inside a screensaver. The Photo Album screensaver (GPhotoShow) seems to be a great candidate. We might approach the author(s) of GPhotoShow and ask them to add hooks to George's code. To be perfectly clear, I'm saying that only one program runs: the GPhotoShow/Prime95 hybrid, not one copy of Prime95 and one copy of GPhotoShow. There must be other ScreenSavers we could investigate. --Luke _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
