Mersenne: G-C-D, F-F-T, P-R-I-M-E !
thanks to Alex Kruppa for suggesting a better modification to the beginning of a GIMPS theme song: GCD, FFT, PRIME! (say each letter separately, singing to mickey mouse theme song tune.) Mary, thanks for pointing out that prime95 counts cycles rather than wall time, so that it will not be obvious when cpu throttles back. Brian, please no more two or three colo[u]r LEDs to indicate status of cpu throttle or anything else. almost 10% of humans has trouble distinguishing colo[u]rs, not to mention the large percentage who don't even know how to spell the word colour properly! for some of us it is practically impossible to distinguish red/yellow/green on an LED, especially when they are flashing. this is often a showstopper problem for me when working with computer/networking/lab devices - i have to find another way to determine the device status, or go find someone who can see colors properly. also, it is good to know that you had a toshiba satellite laptop running for 3 years with no fan failure... but i doubt i will restart prime95 on my wife's toshiba laptop any year soon! and your point is very well taken that a low end cpu chip can handle overclocking better than a high end one. for example, the 1.5Ghz P4 could probably handle it better than the 2Ghz. yes, this was an expensive lesson for me to learn empirically! i thought i was on safe ground due to the supposed thermal protection in the P4, even though i did not have intel motherboard. live and learn. further, as for the stated limits, the Asus utility program does some sort of CPU-probe, and it detected the 2Ghz P4 and said that it could be clocked anywhere from 2Ghz to 2.4Ghz! so what is that about?!? either way, i don't expect intel to replace the cpu and today am planning to pay $280 for a 1.8 Ghz P4 as a replacement. btw, the motherboard was never at 90C, it was the motherboard-cpu-temp-threshold that was set to 90C that was triggering. i don't know if i did anything bad to the voltage regulator with my 5% overclocking... if you or anyone did not see the facetiousness in my blaming prime95 for slaying computers, i'll be more clear: prime95 is not at fault for any of these things. i did all these things with full knowledge of possible risks. thus i am the moron, not prime95! prime95 is clearly imbued with genius (seriously). btw, i have driven over nails before and did not blame my gasoline supplier. once i drove over a harvard students keychain and destroyed a tire. but unfortunately i missed the harvard student. i agree with everyone about on/off cycles being damaging to much computer equipment - especially hard drives. i've always set the power management so the drives always spin when AC power is available. Alan, thanks for the idea about pcmcia fan. i had not known those were available. very cool idea. it is great emailing with all of you folks and participating in the GIMPS project too. a happy safe 2002 to you all, /eli _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Factors
Torben Schlüntz wrote: I'd also like to know about any number fully factorized, whatever size it might be, and whatever size the factor(s) might be. Try Will Edgingtons's page, http://www.garlic.com/~wedgingt/mersenne.html . Use used to keep a comprehensive archive of known Mersenne factors. I am not sure how up to date this files are, but it is a good starting point. Besides I have the question: why does the advanced facor algortithm of prime95 somtimes find 2 factors? This happens eg. at M1289, has 108817410937 and 15856636079 as factors? I'm not quite sure which advanced factor algorithm you mean. There are two possibilities: P-1/ECM: These find all factors that have the required property, i.e. that the starting element in the group has a group order whose factors are only primes and prime powers =B1, and at most one prime =B2. It is perfectly possible to find several factors in one run, or even all factors, in which case the algorithm outputs the input number. Trial factoring: Trial factoring proceeds by trying candidate factors to see if they divide your input number. One normally tests a candidate factor f only after having tried all candidates f (or at least sqrt(f)), so that the candidates can be restricted to primes. For if d|f, d|the input number and should have been found before f. Restricting the f's to only primes is too expensive, so one strikes a balance by excluding only those f which have factors smaller than some limit, in a process called sieving. The optimal sieving limit depends on how fast the sieving can be performed, and how long it takes to test one surviving candidate. Thus, a composite factor can be found if all it's prime factors are above the sieving limit. I do not know what the current sieving limits in Prime95 are, but they surely are 15856636079 for all trial factoring depths. It would be rather easy to test factors for primality once they are found and not print them or comment them as not prime when printed. However, the main purpose of trial factoring in Prime95 is to find smallest factors to eliminate Mersenne prime candidates, here such a test is not neccessary as the smallest factor of a number is always prime. Alex _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: Factors
From: Alexander Kruppa [mailto:[EMAIL PROTECTED]] Torben Schlüntz wrote: ... Besides I have the question: why does the advanced facor algortithm of prime95 somtimes find 2 factors? This happens eg. at M1289, has 108817410937 and 15856636079 as factors? I'm not quite sure which advanced factor algorithm you mean. There are two possibilities: ... Trial factoring: ... balance by excluding only those f which have factors smaller than some limit, in a process called sieving. The optimal sieving limit depends on how fast the sieving can be performed, and how long it takes to test one surviving candidate. Thus, a composite factor can be found if all it's prime factors are above the sieving limit. I do not know what the current sieving limits in Prime95 are, but they surely are 15856636079 for all trial factoring depths. Another issue which used to generate multiple factors by trial division in prime95 (I don't know if it still does) is the following. All factors of Mersenne numbers fall into a small number of concisely describable sets. Prime95 used to test all of one kind of factor in a range before going on to test all those of a different kind in the same numerical range. The program also wanted to find the smallest prime factor. Consider now what happens if two factors in a range belong to different sets. You have to process all sets before you know which is the smallest. Having found any larger ones, it would be stupid not to report them too. Paul _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Factors
Alexander Kruppa writes: Torben Schluntz wrote: I'd also like to know about any number fully factorized, whatever size it might be, and whatever size the factor(s) might be. Try Will Edgingtons's page, http://www.garlic.com/~wedgingt/mersenne.html . Use used to keep a comprehensive archive of known Mersenne factors. I am not sure how up to date this files are, but it is a good starting point. I still keep the data, but have not had time to update the online copies for a while now for several reasons that have nothing to do with GIMPS or other Mersenne stuffs. For example, the current primary cause of my lack of time is my new project at NASA/Ames: the AI-based planning software that I've been helping to develop for the past few years has been selected, this past Nov., for use by the upcoming Mars 2003 rover missions, to assist the human planners figure out what each rover can likely do during each Martian day. When I have time, I also maintain the mers package of programs - all in C source code and as portable as I know how to make them, which, of course, usually makes them slower than the other available programs - to do various things with Mersenne numbers, including verify that factors are prime, factor any composite factors, try to factor Mersenne numbers with Mersenne primes for exponents, etc., as well as the more typical tasks like Lucas-Lehmer tests, trial factoring, ECM, and P-1 of Mersenne numbers themselves. The URL given by Alexander is the primary one, which should have links to all sorts of other things, on my site and several others. Will _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: just some comments to improve our site
On 15 Jan 2002, at 23:26, Torben Schlüntz wrote: Why is P-1 factoring not a single schedule task? like the LL and the Trail Factoring? Why is P1 factoring hooked upon the LL test? Why does P1 not have it's own life like the TF and the LL? I realy hated the P1 until now 21.4 fixed that. I think George has answered those more than adequately. And I hated the CPU-clocks of earlier versions to, because I have no idea what so ever the clock beat of my computer is, but I can relate to time. Ah, but the raw clocks give you a lot of information about the relative efficiency of different systems. In any case, the clock time per iteration is calculated from the raw clocks and the CPU speed (as configured in local.ini - not the actual CPU speed!) and may therefore be misleading - e.g. when a system is running in thermal throttled mode, or a Speed Step (tm) processor is running slow because the system is operating on battery power. Some people might have plenty of mem - outdoing my best a 512M - but some of the machines I (or maybe Primenet) have selected for P-1 have nothing more than 64 or 128M. Which is absolutely fine, unless you're running P-1 stage 2 on 10 million digit exponents - in which case 128 MB is tight, though still feasible. I actually ran P-1 stage 2 on 40025087 on a system with 128 MB (for lack of anything better at the time); it was _very_ tight but did complete. (Yes, it would have run faster with more memory.) We also need a a place for rapid starters. Some Gazelle view. Wow! Even though I've only done 0,323 P90 years I'm number 33 in this week I will certainly continue, because I will catch up with those guys having 79 years Hmmm, maybe in percentage of the week before. I'm not sure what you mean by this. Also the newsletter should more often be sent. We make progress every day so why don't we tell GIMPS'ers what is happening? Even a small progress is a giant leap, like now all numbers below 4.900.000 has been doublechecked or All numbers below 16.000.000 has been trial factorized. The web page http://www.mersenne.org/status.htm already carries this sort of information, updated approximately weekly. Regards Brian Beesley _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: variable iteration speeds
On 15 Jan 2002, at 22:00, Robin Stevens wrote: On an otherwise idle Linux system, I've been noticing that the per-iteration speed has been varying during the course of a single primality test. Until Saturday afternoon I'd been getting a fairly consistent 0.188/0.189s time when the system was idle. It then increased to around 0.206s. It fell again last night to around 0.199s (see logs below - percentages trimmed for 80-character neatness). With stop/start or system reboots between? Some systems appear prone to variability of a few percent from program start to program start. Starting mprime immediately the system boots is usually very good unless the boot included actual partition checks (either forced, or because the partition check interval has expired). When the assignment finishes, the new assignment almost invariably starts at the fastest speed the system will ever run at. In my experience, the speed doesn't change much however long mprime is left running the same assignment, but stopping and restarting can make a significant difference. It might be worth trying that if you find that it's running slow for some unknown reason. Probably the reason for the variability has something to do with the way the program code and data get assigned to physical memory locations. BTW Prime95 behaves similarly under Windows. Regards Brian Beesley _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Slaying Cdplayers for prime95
On 16 Jan 2002, at 2:13, Daidalos wrote: As the current PFC is still going on, and following the experience of the list, I took my beloved computer to a friend's computer store, in order to instal a video card, and thus achieve the speed arranged by great Apollo for a decent P3 at 850. (PFC: Period of Fat Cows). And despite a warning in the back of my head, I only carried the computer, leaving everything else home. I wasn't there whem the technician was trying various video cards to find the fastest combination. But he told me he didn't see the improvenment I told him he should expect in the speed of prime95. Changing the video card won't change the speed of Prime95 much. Prime95 is really dependent mainly on the speed of the CPU, with memory bandwidth also a primary consideration. [This is why you don't get as much improvement as you'd naively expect from just upgrading the processor - the memory bandwidth remains fixed.] Adding a video card - _any_ video card - to systems with integrated graphics may well speed the system up by approximately 10% by removing the graphics load from the main memory bus to the dedicated AGP bus. Adding an AIMM memory module has the same effect - Kingston do a 4MB AIMM for about $5; if you have a mobo using integrated graphics, this is probably the best value upgrade for your system. Maybe he didn't understand well what to look for, but the result was that I brought back the computer without a video card. But alas! The stupid box has Win Millenium in it, and if it is started without all its devices in place, it re-configures itself automatically. The result is that HE has now the stupid impression that there is no CDplayer. (one day I may tell you how you can tell a Microsoft programmer with a flat tire). There is no IRQ conflict, but of course there is a change from the previous IRQ set. When the computer starts, Cdplayer light stays on continuously. Well, if I continue playing around a few days (or, ...weeks? months?), I may eventually find a way to convince my box that there is still a CDplayer. But since I got into this trying to speed up prime95, maybe I am entitled to _some_ technical help? I assume that you have a video subsystem of some sort, else you probably wouldn't be able to boot Windows at all - linux _will_ run on headless systems, but not Windows. In any case, you're going to need a display and console input of some sort (keyboard and/or mouse) to carry out the setup. First of all, switch off unplug the system check that the CD- ROM drive is actually connected to the system. It should be connected to both an IDE ribbon cable and the power supply, and the connections (including the mobo end of the ribbon cable) should be firm. Try pushing them in a bit further - if a connection tightens at all, it might not have been making proper contact. Secondly, check that the IDE cable is connected the right way up - sometimes they will fit either way round - keyed connectors _should_ be, but aren't always, used. The correct way round is with the red marked edge of the cable at the pin 1 end of the socket. Check both drive and mobo ends of the cable. CDROM drives usually have the socket orientation stamped onto the metal plate just above the socket; the mobo socket should have a small 1 printed adjacent to one end of the socket. A torch and a magnifier may help to read the writing on the mobo. If the CD-ROM shares its IDE cable with another device, check that one is set as master and the other as slave. (Or, _both_ are set to cable select on some systems e.g. Dell). If all appears OK after inspection, check the BIOS to make sure that the IDE devices are all set to auto detect. If the CD-ROM is connected to a disabled controller port, it won't work! If all that is OK, Windows should see the CD-ROM drive. If it _still_ appears to be missing, try running the Add/Remove Hardware Control Panel applet. Related to this, I assure you that I will not use the CD to hear music, and thus slow down prime95. The CPU power required to play audio CDs is very low. Regards Brian Beesley _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
SV: Mersenne: Factors
Thanks is a poor word, but anyway thanks to all. I will move on, though my first idea such like: 2kp+1 is a factor when k is 2^x is already dead at M37. :-( damned! I will find another proposal, prove it or disprove it, and continuing getting new ideas. It seems to me that this k (in 2kp+1) is never: 4,12,20,28,36,46,52,60,68,76,84 at least for less than M416.947. Am I again a fool for a pattern already proved? On the other site you can watch this: k=2, 1875 factors in above mentioned space up till M416.947 spanding 35144 primes: k=4, 0 k=6, 1132 k=8, 715 k=10, 465 k=12,0 k=14,233 k=16,351 k=32,138 ... k=64, 65 ... k=72,123 k=74,33 remark, the overall high values of k=2^x factors and remark the low value of eg. k=74. Also remember these factors where obtained by prime95 Advanced factors first of all looking for a low or maybe the lowest value for the factor. So my point here is chance of k=2^x for a factor is high, espcially when p95 has run to the end regarding 64-70 bits low facoring and not found a factor. Now am I wrong in this conclusion and should I drop the the project or is still a small amount of light passing through the halfopen doorway? br happy hunting tsc Try Will Edgingtons's page, http://www.garlic.com/~wedgingt/mersenne.html . Use used to keep a comprehensive archive of known Mersenne factors. I am not sure how up to date this files are, but it is a good starting point. I still keep the data, but have not had time to update the online copies for a while now for several reasons that have nothing to do with GIMPS or other Mersenne stuffs. _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: G-C-D, F-F-T, P-R-I-M-E !
Steve Elias wrote: Mary, thanks for pointing out that prime95 counts cycles rather than wall time, so that it will not be obvious when cpu throttles back. The latest Prime95 includes a date time stamp for each line. Cheers... Russ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Prime freezing when connecting by DSL to Primenet
Hey all, At 01:52 AM 1/12/2002 -0500, Michael Vang wrote: We have been experiencing a similar problem for about 2-3 months... Our belief is that the error is on the server end... I can sometimes duplicate the error by sending large amounts of traffic to PrimeNet... For those experiencing this trouble try ftp://mersenne.org/gimps/p95v22.zip I've fixed a bug in the communication code - the error would have been quite rare. If v21 is working OK, continue using it. The new code uses modified Linux sockets code rather than the old HTTPNET.DLL. If you try this version and still experience troubles, then set Debug=1 in the primenet.ini file and send me an annotated prime.log file telling me what happened. Also, let me know if any other problem occurs! BTW, RPC support is now gone. Thanks, George P.S. If this works, I'll port it to Linux soon. _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
