Re: Mersenne: WinXP SP1 slows prime95
At 09:31 PM 9/10/2002 +, Brian J. Beesley wrote: 2% is the sort of change which can occur when a program is stopped restarted without changing anything else. I check the iteration times pretty often, and when the machine is idle, the times are pretty consistent, less than that 2% difference. Well, it is no big deal, I thought that maybe SP1 added something that was eating up some CPU time. +-+ | Jud McCranie | | | | Programming Achieved with Structure, Clarity, And Logic | +-+
Mersenne: WinXP SP1 slows prime95
Yesterday I went from Windows XP home to service pack 1. The speed of prime95 went down by over 2%. Has anyone else seen this? Any ideas on what caused it or how it can be fixed? +-+ | Jud McCranie | | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: time per iteration
I've been off the mailing list for a while. I just went from ver 21.4 to 22.3 and the calculation of time per iteration seems to be off. I'm running a 15,000,000 exponent on a 1.3 GHz Athlon. It shows (what would be) a remarkable 0.037 sec per iteration, but it takes about 13 minutes for 6000 iterations, which is actually 0.13 sec/iter, 3.5 times as much. The expected completion dates under Status look right. Is there a bug in the per iteration calculation in ver 22.3? +-+ | Jud McCranie | | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: time per iteration
At 10:10 PM 5/26/2002 +0200, Oli wrote: I'm currently running a 33,000,000 exponent if that is of any issue here. (Maybe the per iteration time increases with the size of the exponent to test?) That's it, I'm running a 15,000,000 exponent. +-+ | Jud McCranie | | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: error result
I've been in GIMPS since before the first one was discovered. Today I finished an exponent, and saw some stuff I haven't seen before. After it completed, it said M14776187 stage 1 complete ---transformations --- time starting stage 1 GCD stage 1 GCD complete ERROR: factor doesn't divide N! contacting server etc. What went wrong? It looks like at the end of the L-L test, it did a GCD, thought it found a factor, but it wasn't a factor. For a while during this exponent, I had quick user switching on with WinXP. When I realized that prime95 was running twice as slow, I figured out that quick switching was causing two copies of primr95 to run. Could that cause a problem? +-+ | Jud McCranie | | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: error result
At 04:04 PM 5/24/2002 -0400, George Woltman wrote: Well another bug was fixed in 22.3. Is that available? The download page says version 21. +-+ | Jud McCranie | | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: error result
At 08:41 PM 5/24/2002 +0200, Dieter Schmitt wrote: The help file says this bug was fixed with version 20.5 concerning P-1 or ECM. I'm using ver 21.4.1. +-+ | Jud McCranie | | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ 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
At 11:31 PM 1/11/2002 -0600, Steve Harris wrote: Interesting... I have had that happen to me as well a few times with PCs on a DSL (but without AOL). It doesn't happen on a regular basis but does lock up the program (v21.3) for hours or days at a time. I've been using Prime95 with DSL for about 16 months, and AFAIK, it has never happened to me. ++ | Jud McCranie | || | former temporary part-time adjunct | | instructor of a minor university | ++ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: But....but...when is 3^x - 2 prime?
At 05:26 PM 12/6/2001 -0500, Paradox wrote: 1) I have a P4 1.9 GHz with PC800 ram that is testing an exponent in the 333X range, and it is getting approximately 0.180 sec/iteration when completely idle on Windows 2000. According to the benchmark on mersenne.org, it should be around 0.143. Am I losing cycles somewhere? Is it possible the mainboard (Intel 850GBC) is lying to me about the clockspeed? Do you have an actual video card or is the video on the motherboard (sharing memory)? That can be a factor. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: HD crash
My hard drive crashed, and I have almost certainly lost all of the GIMPS data for the exponent I was working on and 4 more I had in the queue. The initial trial factorization had been done on all of them and the first one was just about 4 days from completion. What should I do about these lost exponents? (I don't know which ones they were) +-+ | Jud McCranie| | | |Thought I saw angels, but I could have been wrong. Ian Anderson| +-+ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: M#39 news!
At 05:47 PM 12/1/2001 +0100, Alexander Kruppa wrote: Look like the cat is out of the bag now - it's 2^13,466,917 - 1. Was this early publication indended? I thought the press release was due only after the independent double check completed, but then they quote Tim Cusak of Entropia, which makes it sound like an official announcement. Or is the official double check finished already? The independent check was supposed to be completed today, so maybe it was. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Will a mainframe ever hold the record again?
Do you think that a mainframe computer will ever again hold the record for the largest known prime, or will they be unable to compete with thousands of personal computers in a distributed project? Just wondering. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: Will a mainframe ever hold the record again?
At 03:29 PM 11/28/2001 -0500, Donald Rober wrote: BUT I doubt that anyone is interested in giving up that much computing power on those machines. That's what I thought too. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: start Prime95 at bootup
I used to have Prime95 starting at bootup on my Windows XP system. I had some problems, though, and now Prime95 doesn't start at bootup. It is not listed under msconfig as it used to be. I have start at bootup checked. I deleted prime95 and reinstalled. How can I make it start at bootup (it used to do that). +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: [Mersenne] celebrate
I should have suggested this yesterday, but let's have a meteor shower to celebrate the probable discovery of a new Mersenne prime! +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: prime
There has been an unverified prime reported! It passes the 32-bit security code that comes on every results.txt line. This is not overly difficult to forge though. The user reporting the prime has completed 3 other LL tests I think it is quite interesting if this is only his/her 4th LL test! Of course we all appreciate the people who are able to devote several CPUs to the job, but this is encouraging to the little guys. It shows that every little bit helps! +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: timings
At 06:47 PM 11/10/2001 -0500, Carleton Garrison wrote: I have a Dell Inspiron 8000 with a ATI Mobility M4 which I'm pretty sure is PCI. As George and I found out, the problem is when the video card is sharing your main RAM. Do you know if yours does that? +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: timings
At 08:05 PM 11/10/2001 -0500, Carleton Garrison wrote: It wouldn't be so bad if my times majorly improved when my monitor shuts down... Right now my iteration times are 36% longer than when the video is off. When I was using 32-bit color instead of 16 (as I am now) the difference was about a factor of 2. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: timings
At 02:39 PM 11/10/2001 -0500, Carleton Garrison wrote: Well, this means almost 58% slower than expected. Well, I hope you figure it out because the same has happened to me. Is your video on the motherboard? +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: What will we do when anyone finds a number of 10 million+ digits which is prime?
At 12:02 AM 11/5/2001 +0100, =?utf-8?Q?Torben_Schl=C3=BCntz?= wrote: It will be kind of difficult to find new volunteers that will use time and electricity to fill the hole if nothing more than glory is won. I'm not in it for the prize, and a lot of others aren't either. I've been it over 4 years (maybe over 5 years?), well before there were any prizes. I just replaced a computer that I have been using over 4 years, and I think I was in GIMPS before I had that one. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: What will we do when anyone finds a number of 10 million+ digits which is prime?
At 01:43 AM 11/5/2001 +0100, Steinar H. Gunderson wrote: Speaking of which -- shouldn't we be (statistically) really close to finding a new prime soon? Yes, statistically. You'd expect the next one to be before 14,000,000 and I've got assignments in the 13,000,000 range. However, all exponents have been checked once only to a little past 8,000,000. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: What will we do when anyone finds a number of 10 million+ digits which is prime?
At 08:48 PM 11/4/2001 -0500, Nathan Russell wrote: Of course, this whole argument makes (as far as I can see) heavy use of the gamblers' fallacy, aka the fallacy of maturation of probabilities (Hey, I lost the last 50 games - what are the odds against me losing 51 5-man games in a row? I'm certain to win!) Statistically, each exponent resulting in a prime is about twice the previous one. There is a heuristic argument that supports that being the case. The last one was 6.9 million something, we're now testing close to twice that. I think there are only three cases where one exponent is more than twice as large as the previous one. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: Mersenne Digest V1 #895
At 08:46 AM 10/27/2001 +0100, Gareth Randall wrote: I'll answer to the group as well since this is a very useful tool for prime95 users. Yes, it is great. On Windows XP ctrl-alt-del shows that information (maybe on Win 2000 too). However, WinTop puts blanks for zero percentages whereas ctrl-alt-del on WinXP shows 00. It doesn't even omit the leading zero. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Task Manager
At 09:37 PM 10/27/2001 +0200, Hoogendoorn, Sander wrote: On both W2K and XP you also have to press the Task Manager Button, or press ctrl-shift-esc to go there right away C-S-esc doesn't work for me, but C-S-Del and then the Processes tab. If you close with the processes tab selected, it comes back up that way. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: [Mersenne] video can affect Prime95 speed
Your computer's video may affect the speed of Prime95! This applies to systems with video on the motherboard, sharing your main memory. George Woltman says it is because of the memory bandwidth used for video. Two weeks ago I got a 1300MHz Athlon, with 384MB of PC133 RAM. The video is on the MB, it shares memory. I noticed that the benchmarks were about half as good they should be! I discussed it with George, and he came up with the idea of testing the video. Here are per iteration times for 13,500,000, based on video mode: resolution color depth MB video memory time (sec) 1280x1024 16 bits 2.5 0.237 1024x768 32 bits 3.0 0.204 800x600 32 bits 1.8 0.171 1152x864 16 bits 1.9 0.168 1024x768 16 bits 1.5 0.156 800x600 16 bits 0.9 0.140 Generally, the more video memory used, the slower Prime95 runs. I have the power saver cut off the video after 10 minutes, and then the iteration time goes down to 0.121 seconds - almost twice as good as the worst time, and along the times for other Athlons of similar speed. So if you are buying a computer, it is better to get one with a real video card. If you're running Prime95 on a computer that has video built in to the motherboard, try this experiment, and have the video turn off after a few minutes of inactivity. Also, you can consider using a lower resolution or color depth if you want higher performance from Prime95 while you're using the computer. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ 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: Re: 26 exponents
At 08:23 PM 5/14/2001 +, Brian J. Beesley wrote: On 14 May 2001, at 8:45, Nathan Russell wrote: 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. Sorry, I don't buy that. Every system has exactly the same chance of picking up any given assignment; it's a matter of the time at which you make the request. Under your proposal, exponents would be double assigned. A 200 MHz system and a 1.2 GHz system calling in at about the same time could get the same exponent. But the one with the elite fast system would in effect get the first LL test and the non-elite system would get the DC. Also, if you have a 200 MHz and a 1200 MHz working on the same exponent, if it turns out to be a new prime the 1200 will show that first. Then someone with a fast machine will run a DC before the 200 machine can finish it. I know you said that the 200 still gets credit, but if a prime is reported, we don't want to wait several (possibly many) more months for a DC. Under my proposal, newcomers would get a first time LL test - they just wouldn't get an exponent that someone else had abandoned. That is not to keep newcomers from contributing - they even get to do first time LL tests (and be assured of that) - it is try to keep an exponent from being abandoned more than once. ++ | 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: Re: 26 exponents
At 09:44 PM 5/14/2001 -0400, Nathan Russell wrote: However, that is still drawing a distinction between new and experienced users. Well, so what if it does? It is an extremely minor difference. New users would still get first time LL tests - it just means that they wouldn't get exponents that someone else abandoned. It is an exponent thing, not a user thing. Many organizations have distinctions for new members. Non-voting members, provisional members, Fraternity pledges, etc. To a new user, what does it matter if he gets a brand new exponent instead of one that someone else abandoned in the same range? Why would a new user prefer an exponent someone else abandoned over one that no one else has been assigned? To me, it seems that (if anything) he would prefer a new one because there is a possibility of the person who abandoned it getting back to work on it and finishing it in the mean time. For that matter, if a milestone is delayed by a month or two, it doesn't significantly hurt everyone's overall odds of finding a prime. I know, but it would be nice to know whether what seems to be M38 is or isn't M38. I can empathize with you here. However, I was a new user only a little over a year ago, and if someone had said on the mailing list at that time that new users should be given assignments chosen so that they couldn't harm milestones, I would have been upset. They would still be contributing towards milestones. If there are exponents below a milestone that never have been assigned, they would get them. Yes, it would be nice to say that we know for sure which Mersenne prime is the thirty-eighth, but doing so does not speed us towards discovering the thirty-ninth. 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. For that matter, I am sure that there are users who have run a single exponent and then left, Well, that's OK. Their work helps. Does anyone have an idea of the % of people who start and then quit w/o finishing an assignment? ++ | 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: Re: 26 exponents
At 09:44 PM 5/14/2001 -0400, Nathan Russell wrote: However, that is still drawing a distinction between new and experienced users. 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? ++ | 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: missing exponents?
At 10:22 AM 5/12/2001 -0400, George Woltman wrote: Dietmar's guess was accurate. Six weeks ago there were grumblings on the list that we were making slow progress on double-checking milestones. I promised to make monthly checks of my database and the server's database and make exponents available for triple-checking when necessary. Checking the status page, we seem to be stuck on 26 exponents between 6,325,000 and 6,972,593 - that haven't had one LL test. I've been double checking exponents in this range for months (and getting them done at the rate of more than 1 per month). I've been double checking because that is work makes the most sense, but does it make sense to double check this range when there are untested ones? If these 26 were actually being tested, they would be knocked off at the rate of at least one per day, and it has been a while since one has been finished. ++ | 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: missing exponents?
At 04:52 PM 5/12/2001 +0100, Chris Jefferson wrote: Haven't we had enough discussions about taking bnumbers people are takingf a long time to test / not chexcking uin very often? :) Sorry if that has been covered, but I just got back on the list after being off for several months. ++ | 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
Mersenne: Re: 26 exponents
At 01:49 PM 5/12/2001 -0400, George Woltman wrote: There were 37 on April 15 and 59 on March 11. With a little patience we will get there. OK. My 300 MHz P-II has been doing double checks for months and it does one of that size in about 20 days or so. Since only 9 have been finished in the last 28 days either the remainder are running on much slower machines than mine, or they have been abandoned. The makes the most sense assignments are based strictly on CPU speed. My theory is that the average user with a slowish machine would rather complete one double-check in a month or two rather than wait 4 times as long for a first time check. That's true. My last first-time check took 3 months, which is why I went to double checking, which take about 3 weeks. ...All 4 results will be returned in 44 days. Great! ++ | 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
Mersenne: Re: 26 exponents
At 01:49 PM 5/12/2001 -0400, George Woltman wrote: In my last email, I alluded to how the server has some strange behavior when the double-checking and first-time testing ranges overlap. One such glitch is that if one of these 26 exponents expires, it is reassigned as a double-check (and will have to wait until all lower exponents are assigned). A thought (but it would mean more work) is that if an exponent expires, it gets reassigned to someone who has completed at least one exponent, to keep the progress going. These unfinished exponents in the 6,000,000 range were originally assigned so long ago that they must have been dropped several times. ++ | 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: Re: 26 exponents
At 03:26 PM 5/12/2001 -0400, Nathan Russell wrote: I think that's more of a 'quick fix', and might make new participants feel that GIMPS doesn't trust them. Yes, but a new user need not know that they don't get an exponent that has expired until they have finished an assignment. My point is that if an exponent is dropped, it could be reassigned to someone that has shown a willingness to finish it. I've been steadily working on GIMPS for nearly 5 years, always 1 fulltime machine, occasionally 2. I've been doing doublechecks in the 6,000,000 range for a few months because I use a 300 MHz machine. I know doublechecking is important. But then I see these few gaps under M38? and I think I could have done several of those. I know there are going to be a lot of people who start GIMPS and drop it, and I know that that the gaps will eventually be filled in. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: missing exponents?
At 08:14 PM 5/12/2001 +, Brian J. Beesley wrote: rather small, so the reason a third or fourth run is neccessary is very probably because results with mismatching residuals are being submitted for some reason. Most probably random glitches? Another nice thing would be if people who have submitted several results that don't match other people's results they could be notified that they may have a hardware problem. ++ | 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: Re: 26 exponents
At 08:44 PM 5/12/2001 +, Brian J. Beesley wrote: I don't like the idea, for the reason Nathan indicates - it smacks of elitism. A better fix would be to patch PrimeNet so that it can assign an exponent for two LL test runs simultaneously. (Whichever finishes first becomes the LL test, the other is the double-check). But that also seems elitist. If you've got a 1.0 GHz system and the other person has a 1.2GHz system, you're relegated to the double check because your system is a little slower. The other way the elite would be the ones who have completed at least 1 exponent. I think of that more as productive or reliable than elite. _ 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
I don't like the idea, for the reason Nathan indicates - it smacks of elitism. By my idea, new users would get untested exponents - they just wouldn't get one that had already been abandoned. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: P4 speed and implications thereof
At 07:07 PM 2/11/2001 -0500, Nathan Russell wrote: My understanding is that they are designed to perform well for graphical tasks; in my experience, people will buy even very expensive computers if it improves the performance they see when doing graphical tasks; gaming in particular comes to mind. From what I hear, the P4 is better than the Athlon at streaming data, but worse at everything else. Streaming data is good when you process a lot of data the same way, such as in graphics. But the P4 has a deep pipeline that will be dumped if there is a branch. If I were buying now, I'd get an Athlon. That might change in a few months. +---+ | Jud McCranie | | | | Think recursively( Think recursively( Think recursively)) | +---+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: P4 speed and implications thereof
At 06:12 PM 2/11/2001 -0500, Nathan Russell wrote: Additionally, the P4 is only going to get faster in the next year or two. This frankly makes me wonder how much longer there will be a place in GIMPS for slower machines. I wonder how many people are going to have P4s. Presently, the Athlon is faster for most things, and cheaper. I don't know if the P4 will pull ahead of AMD chips for most things, so will people buy them? +---+ | Jud McCranie | | | | Think recursively( Think recursively( Think recursively)) | +---+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: screen savers
At 08:14 PM 2/9/2001 -0500, Nathan Russell wrote: The thing here is that this would make the rate of progress slow. I know that when I first started GIMPS, I got a little depresseed thinking things like "I've been here an hour and it's not even a third of a percent done!" When I joined, I was getting a LL test in about 9 hours on my P-60. Now it takes 3 months on my P-300. +---+ | Jud McCranie | | | | Think recursively( Think recursively( Think recursively)) | +---+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Overclocking - bad for project?
At 10:31 AM 12/23/2000 +, Gareth Randall wrote: However, surely this project is one where overclockers do more harm than good? When you're running your favourite game, it doesn't matter if a couple of incorrect calculations creep in, but the Mersenne project involves very long calculations with basically a boolean answer at the end. ... I agree. I've never overclocked my computers because I think it is more important to be confident in the results. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: P4
I understand that the SSE2 instructions operate only on 64-bit (and 32-bit) floating point data, whereas the FPU registers support 80-bit intermediate results. I know this is a little off-topic, but how good is the P4 at integer operations? _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt
Re: Mersenne: P4 - a correction
At 11:05 PM 11/27/2000 -0500, George Woltman wrote: A question for readers. Prime95 currently uses about 8MB (exponent around 11 million). How would you feel if the P4 optimized version used 13MB? 23MB? 33MB? Larger memory use would be OK with me, since I have 320MB. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: pi
At 12:06 AM 2/9/00 -0600, [EMAIL PROTECTED] wrote: But when I look at a circle I see a finite area within the circle with no means of growing or escape. Logic seems to indicate that pi would have to be a finite exact value since the area in the circle is finite. No, pi is irrational, which means that the digits go on forever without repeating. So, either the figure for pi is in error (not likely) or pi has a end. The calculated value of pi is never exact, since it is calculated to a finite precision. ++ | Jud McCranie | || | 137*2^197783+1 is prime! (59,541 digits, 11/11/99)| | 137*2^224879+1 is prime! (67,687 digits, 1/00)| ++ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: PI is a transcendental number
At 09:58 AM 2/10/00 +0800, Low Hwee Boon wrote: 6. But most irrational numbers can be obtained from solving a polynomial equations Actually almost all irrational numbers are transcendental, and therefore not the root of a polynomial with rational coefficients. ++ | Jud McCranie | || | 137*2^197783+1 is prime! (59,541 digits, 11/11/99)| | 137*2^224879+1 is prime! (67,687 digits, 1/00)| ++ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Version 20 memory questions
At 11:38 AM 1/31/00 -0500, George Woltman wrote: Would we be better off disabling P-1 factoring unless the user explicitly activates it (knowing that most users won't read enough to turn it on)? That sounds like a good idea to me. Giving up 24-48MB would interfere with some people's work, and you don't want to do that. Prime95 needs to be transparent. It probably should be in the advanced menu, and allow you to set the hours and days. ++ | Jud McCranie | || | 137*2^197783+1 is prime! (59,541 digits, 11/11/99)| | 137*2^224879+1 is prime! (67,687 digits, 1/00)| ++ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Size of largest prime factor
At 11:48 AM 1/24/00 +0100, Paul Landon wrote: On the average, the largest prime factor of n is n^0.6065, But for Mersennes this might not be the case. For the size of exponents that we deal with Mersennes are less composite than a random set of ones zeroes. That's right, but the original question just said a large random number. ++ | Jud McCranie | || | 137*2^197783+1 is prime! (59,541 digits, 11/11/99)| | 137*2^224879+1 is prime! (67,687 digits, 1/00)| ++ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Size of largest prime factor
At 03:48 PM 1/23/00 -0500, Pierre Abbat wrote: If I pick a huge number n at random, how much smaller than n, on average, is its largest prime factor? On the average, the largest prime factor of n is n^0.6065, and the second largest is n^0.2117. Reference: Knuth, the Art of Computer Programming, vol 2, section 4.5.4. ++ | Jud McCranie | || | 137*2^197783+1 is prime! (59,541 digits, 11/11/99)| | 137*2^224879+1 is prime! (67,687 digits, 1/00)| ++ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: Size of largest prime factor
At 04:51 PM 1/23/00 -0600, Kyle Evans wrote: But (assuming n is composite) no prime factor of n can be greater than n^0.5. So how can n^0.6065 be the average? I'm not assuming that n is composite. Some of them are prime, and in that case the largest prime number is the number itself, and that brings up the average. ++ | Jud McCranie | || | 137*2^197783+1 is prime! (59,541 digits, 11/11/99)| | 137*2^224879+1 is prime! (67,687 digits, 1/00)| ++ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: 8087 control word
I just messed with a program that alters the 8087 control word, then I realized that this could affect Prime95. Would a program that alters the 8087CW interfere with Prime95? ++ | Jud McCranie | || | 137*2^197783+1 is prime! (59,541 digits, 11/11/99)| ++ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: The Second Mersennium...and sequences
At 09:35 PM 1/12/99 +, Daniel Grace wrote: On the more relevant issue of storing Mersennes is this question and storing numbers from Mathematical series (particularly primes) in general is: Has anyone worked out an efficient way to compress the primes or prime exponents that produce prime Mersennes? I doubt that the Mersenne exponents can be compressed much. As far as a general prime list, there are several ways to save space. One is to store the gaps between primes instead of the primes themselves, and reconstruct the primes as you read through the list. One byte for the semi-difference suffices to fairly large primes. Another way is to use a bit vector indicating whether the given number is prime or not. Which method is best depends on the size of the list, and how you want to use the list. ++ | Jud McCranie | || | 137*2^197783+1 is prime! (59,541 digits, 11/11/99)| ++ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: Re: The Second Mersennium Behind Us, How Now For MyriadThe Third?
At 04:47 PM 1/11/00 -0700, Aaron Blosser wrote: 'Tis true. It doesn't surprise me that many companies are teaming up to fight the patent. Windowing was *the* best way to quickly fix all that software, and a good number of software vendors used it. If I recall right, the guy who owns the patent wasn't asking for much in the way of royalties from each company (but amounts to a lot when totalled), but I think the fight revolves around whether this guy really invented the idea, or whether it's just one of those common sense things that can't be patented, or something like that. This is getting off topic, but: The criteria for something to be patentable is that the average practitioner in the field wouldn't think of it. So it boils down to whether the average programmer would think of windowing, given the problem. ++ | Jud McCranie | || | 137*2^197783+1 is prime! (59,541 digits, 11/11/99)| ++ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: The Second Mersennium Behind Us, How Now For MyriadThe Third?
At 09:54 PM 1/11/00 +, Steinar H. Gunderson wrote: Dunno 'bout all that, but another problem was that in order to do a "quick and dirty" fix of the Y2K problem, a good number of people implemented windowing. The funny thing is, somebody has actually been granted a patent on this. Whoops! I'm violating someone's patent! (Don't tell anyone.) ++ | Jud McCranie | || | 137*2^197783+1 is prime! (59,541 digits, 11/11/99)| ++ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: Re: The Second Mersennium Behind Us, How Now For MyriadThe Third?
At 04:47 PM 1/11/00 -0700, Aaron Blosser wrote: Off topic, but: If I recall right, the guy who owns the patent wasn't asking for much in the way of royalties from each company (but amounts to a lot when totalled), but I think the fight revolves around whether this guy really invented the idea, or whether it's just one of those common sense things that can't be patented, or something like that. MSNBC online probably has a story on it in their tech section. Ah...sure enough: http://www.msnbc.com/news/72.asp . " Dickens applied for the patent in October 1996 " I was using windowing in 1987, so his patent is invalid (prior invention). ++ | Jud McCranie | || | 137*2^197783+1 is prime! (59,541 digits, 11/11/99)| ++ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Fibonacci Series
At 04:50 PM 12/18/99 +0100, François Perruchaud wrote: An old book of mine gives without proof an example of Fibonacci Sequence that countains no primes, but where U(1) and U(2) are co-prime. The sequence was found by R. L. Graham. Reference : A Fibonacci-like sequence of composite numbers, R.L. Graham, Math. Mag. 37, 1964. U(1) = 1786772701928802632268715130455793 U(2) = 1059683225053915111058165141686995 U(N+2) = U(N+1) + U(N) I only verified with Mapple that U(1) and U(2) are co-prime and that U(N) is composite for N10. I checked a few thousand terms, and they were all composite. ++ | Jud McCranie | | | | 137*2^197783+1 is prime! (59,541 digits, 11/11/99) | ++
Re: Mersenne: Atanasoff
At 01:57 AM 11/25/99 -0500, Vincent J. Mooney Jr. wrote: There seems to some interest in the first computer. I refer you to the book "The First Electronic Computer : The Atanasoff Story" by Alice R. Burks, Arthur W. Burks still available on amazon.com. That book is controversial, and most people in-the-know don't agree with it. ++ | Jud McCranie | || | 137*2^197783+1 is prime! (59,541 digits, 11/11/99)| ++ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Maple
At 01:12 AM 11/27/99 +, Ian L McLoughlin wrote: Anybody know about this language? Where it can be obtained...et..al.. There's information about it at: http://www.maplesoft.com/ I got my copy from an online book store. ++ | Jud McCranie | || | 137*2^197783+1 is prime! (59,541 digits, 11/11/99)| ++ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Atanasoff
At 07:31 PM 11/28/99 -0500, Vincent J. Mooney Jr. wrote: Pleasse tell us what there is to disagree with. This is off-topic, but there was prior work on the Mark I, in Germany by Zuse, and in England on the code breaking project. There is no clear inventor of the computer in the eyes of most historians. Much of the controversy is covered in chapter 8 of "ENIAC" by Scott McCartney and other books such as ""Portraits in Silicon". Iowa State University seems overzealous in promoting Atanasoff. +----+ | Jud McCranie | || | 137*2^197783+1 is prime! (59,541 digits, 11/11/99)| ++ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: RE: PI and other periods
At 12:09 PM 10/21/99 +, Steinar H . Gunderson wrote: overtime... But again MAYBE, there is a real period to that number... No. As far as I know, there is a proof saying that pi has no periods. If pi was periodic it would be rational, but pi is irrational. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: estimating mersenne primes
At 01:01 PM 10/21/99 -0500, Tony Pryse wrote: This is **not** the correct way to fit an exponential when you have "real" (i.e., experimental) data. What is the correct way? I've been taking logs and then doing a linear regression, but what is the correct way? +-----+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: PI
At 01:36 PM 10/21/99 -0500, Herb Savage wrote: I remember reading an interview with the Chudnovsky brothers a long time ago. I think they had computed about 4 billion digits at the time. Then they felt that there would be something interesting in the digits of PI if you computed them out far enough. They thought that this might happen by the time you got to 1 trillion digits. I don't know if that makes much sense. If you do get something significant after a finite number of digits, it is probably a statistical fluke and won't hold up in the long run. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: estimating mersenne primes
At 06:07 PM 10/20/99 -0400, Darxus wrote: Okay, so I got my line of log base 2 of the exponents of the 1st 37 mersenne primes. I took those numbers did a linear extrapolation, and did a 2^n to the resulting extrapolated numbers. I then went back and did my exponential extrapolation to the exponents of the 1st 37 primes. I was pretty surprised that the extrapolations for M38-M42 (all that I did) were *exactly* the same for both methods of extrapolations, Your two methods are equivalent. I still wanna know why extrapolating off of the number of digits, instead of the actual exponents, gave me a number closer to 6972593 (38th discovered mersenne prime). I dunno, coulda just been a coincidence. Probably so. If you use the number of digits in one method and the actual exponents in another, the predictions will differ slightly. One of them will be closer to the true value. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Modular arthimatic..
At 06:25 PM 10/15/99 +0100, Chris Jefferson wrote: Consider a general number (odd) number c which can be factored into ab=c W.L.O.G. assume b is greater than a then let x=(a+b)/2 , y=(b-a)/2 then (x+y)(x-y)=c x^2 - y^2 = c x^2 = c + y^2 So if we can find if this equation has any integer solutions, we've found our factors... Good idea, but this is Fermat's factoring method. It works pretty well if a and b are close. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Islands of Truth
At 09:57 AM 10/14/99 -0400, [EMAIL PROTECTED] wrote: The supposed clustering is in fact typical of 'random' data. Didn't someone on this list test the data for randomness using a Poisson distribution a few months ago? +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Error 11
I just communicated with the server, and got error 11 - exponent already tested on one I'm 95% through with. (A few weeks ago I had to transfer some exponents from one machine to another, so something may have gotten mixed up in the process.) Will this still count as a double check of that exponent? I have some other exponents queued up (that I transferred) - would the communication with the server warn me if they have been tested? +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Vaxen Intel
At 10:29 PM 10/12/99 -0500, Ken Kriesel wrote: What sort algorithm are those figures for? In what programming language? Which compiler? It was insertion sort, based on Bentley's pseudocode, so it was the same algorithm. I coded it in Pascal, he did it in C. I used Stony Brook Pascal+ ver 7.10, I don't know what compiler he used, but it was probably the standard C compiler for the VAX. There are lies, damned lies, and statistics. Then there are benchmarks... There are some variables that are not accounted for. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Factoring
At 04:27 PM 9/21/99 -0700, Eric Hahn wrote: We know that any factor of 2^p-1 is in the form 2kp+1. Letting x =2, Can (2kp+1)^x = 2^p-1 ?? Can (2kp+1)^x * (2kp+1) ... = 2^p-1 ?? No known factors of Mersenne numbers have x1, but it hasn't been proven that it is impossible. +-+ | Jud McCranie| | | | Programming Achieved with Structure, Clarity, And Logic | +-+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Evil, evil prize thread
At 04:40 PM 7/25/99 -0400, Jeff Woods wrote: While I agree with this, if the effort does NOT fragment and jump ahead to potential 10MM-digits, someone else is likely to find and claim that $100K with a Proth prime, since checking those will take far less time than a Mersenne test of the same order. Is that true? I thought that a LL test of a Mersenne was faster. ++ | Jud McCranie | || | 127*2^96744+1 is prime! (29,125 digits, Oct 20, 1998) | ++ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Proth's Test (was: Re: Mersenne: Evil, evil prize thread)
At 07:13 PM 7/25/99 -0400, Chris Nash wrote: That bit is virtually free of charge. Any quadratic non-residue will do just fine. But you don't easily know if a number is a QNR, do you? +--+ | Jud "program first and think later" McCranie | +--+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Factoring LL tests
At 01:10 PM 7/18/99 -0400, Geoffrey Faivre-Malloy wrote: I was reading Fermat's Enigma today and something occurred to me...would it be possible to work with a number quicker if we used a higher base? I.E. Use base 32 instead of base 10? Multiple precision arithmetic operations do that. +--+ | Jud "program first and think later" McCranie | +--+ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Benford's law (was exp. representations)
At 12:38 AM 7/13/99 -0400, Lucas Wiman wrote: Here are the percentages for the first 3000 powers of 2. The first collumn is the percentage, the second is the difference from the predicted Benford percentage. Weird, I would have thought that it wouldn't affect powers of two... That's the type of thing that follows the law precisely in the long run. (the repeated multiplications). A way to look at this is to think of a slide rule (if you remember them). Anything that has a uniform distribution on the slide rule follows Benford's law. The distance from 1.0 to 2.0 on the slide rule is 0.301... of the length of the scale, etc. A repeated multiplication by a number other than 0 or 1 gives a uniform distribution along the scale of the slide rule. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: re: Mersenne prime exponent binary
At 09:05 AM 7/13/99 -0400, Chip Lynch wrote: In some vague attempt to not take the Benford issue off topic, it's interesting that numbers 2^n (for all Natural numbers n) follows the pattern VERY closely, In the limit as n - infinity, 2^n must follow the law exactly. Almost by definition. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: re: Mersenne prime exponent binary representations and 1's frequency (incl M38)
At 11:55 AM 7/12/99 -0400, Chip Lynch wrote: I'm not sure what the law of leading digits is, but I read this as talking only about base 10 numbers... so the leading digit 1 is compared to leading digit 2, 3, 4, ..., 9. Right? So for numbers 2^n (in Base 10), [or is it 2^p?] there are a lot more leading ones than one would "expect" naievely (you would expect 1/9 to start with "1", I imagine). Why this is, I have no idea... can someone explain? It is also known as Benford's law and the First Digit law. You can read about it at Eric's Treasure Trove of Math (seems to be down right now or I'd give the URL). It would take me a few paragraphs to explain, but I'll do it if you can't find it elsewhere. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Mersenne numbers
At 10:16 AM 7/9/99 -0700, Kris Garrett wrote: Has it been proven that all mersenne numbers greater than one are square free? As far as I know, it has not been proven (and no repeated factors are known either). +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Head's algorithm for multiplying mod n
At 06:51 PM 7/9/99 +0100, Brian J. Beesley wrote: For reasonably small multi-precision numbers, Head's method is actually very good, if you're working on a true RISC processor with no integer multiply instruction. I started using Head's algorithm in 1981 on my Apple II. It was better than triple- and quad-precision routines. It has propagated through my software, and I've assumed that it is still preferable. I probably need to reevaluate it on a Pentium. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Head's algorithm for multiplying mod n
At 06:19 AM 7/8/99 -0400, you wrote: All, In the book _Primes and Programming_ Head's method of multiplying two numbers mod n is mentioned. Is this actually more effiecient than simply multiplying the two numbers and taking the modulus? Yes, because it keeps the numbers smaller. It was originally: Method from Multiplication Modulo N, by A. K. Head, Bit 20 (1980) 115-116 +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Infinitude of Sophie-Germains]
At 11:52 AM 7/8/99 -0700, Rudy Ruiz wrote: I am not aware that anyone has yet proven the infinitude of Sophie Germain Primes. [Granted that, in itself, does not mean anything ;) I was wrong. As far as I know, it hasn't been proven either (but it is almost certainly true). I had seen a conjectured distribution function that went to infinity, but it has not been proven. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Head's algorithm for multiplying mod n
At 08:11 PM 7/8/99 -0400, Pierre Abbat wrote: That is going to be a *lot* slower than FFT convolution, for numbers the size of the Mersenne numbers we're testing! Head's algorithm is for getting x*y mod n when 0=x,yn; and n is such that nM but n^2M, where M is the largest integer you can store in a format native to the computer. I don't think it applies for Mersenne testing, but it helps a lot with Fermat-type tests (pseudoprimes, etc). +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: question
At 10:47 AM 7/6/99 +0200, Benny.VanHoudt wrote: Now lets only focus on the set 2^p - 1 with p prime, i.e., the set of numbers that we are checking out at GIMPS. Has anyone proven that an infinite number these are NOT prime (this is VERY likely to be true)? If so, how can one prove this easily (it is probably not possible to indentify a subset that is NOT prime as above because then we would not consider all of them for GIMPS)? If 2p+1 is prime then it divides 2^p-1. If it has been proven that there are in infinite number of prime pairs p and 2p+1 then this proves that there are an infinite number of 2^p-1 that is not prime when p is prime. These are called Sophie Germain primes, and it has been proven that there are an infinite number of them, therefore there are an infinite number of composites of the form 2^p-1 when p is prime. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: question
At 06:55 PM 7/6/99 +0100, Brian J. Beesley wrote: Can you please supply a reference to this proof? Chris Caldwell's Prime Pages show this as a conjecture (with a strong heuristic argument). No, I was wrong about it having been proven. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: distribution of factors (was 10,000,000 digit prime)
At 03:05 AM 6/30/99 -0400, Lucas Wiman wrote: I realize this is probably a FAQ, (and I intend to put it there), why is the distribution of factors so non-linear? Because small factors are more likely to divide a given number. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Mersenne FAQ 1.1
At 04:16 AM 6/29/99 -0400, Lucas Wiman wrote: All, Here is version 1.1 of the FAQ. Here's a question that needs to be addressed: how to go from digits to exponents, and exponent to digits. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Mersenne FAQ 1.1
At 04:16 AM 6/29/99 -0400, Lucas Wiman wrote: All, Here is version 1.1 of the FAQ. Also. FAQs involve why do we think there are an infinite number of Mersenne primes, how many are expected below a given limit, and what s the probability of finding one. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: PrimeNet Stats Updated
At 11:17 PM 6/29/99 +0200, Steinar H. Gunderson wrote: Then what is the best fit? Exponential? :-) It is slightly parabolic. The good news is that it is trending upward faster than linearly. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: Status estimate
The Status estimate of the chance that the number you are testing seems to be off by a factor of e, based on Wagstaff's estimate. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: LL Factoring DE Crediting
At 09:59 PM 6/28/99 +0100, Gordon Spence wrote: The GIMPS home page explains the following "Finally, if a factor is later found for a Mersenne number or the Lucas-Lehmer result is found to be incorrect, then you will "lose credit" for the time spent running the test." It is on www.mersenne.org/top.htm always struck me as odd I must admit. It isn't very clear, but the purpose may have been to discourage bogus positive results, because they will eventually be double-checked. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: A few questions
At 12:14 PM 6/27/99 -0400, Geoffrey Faivre-Malloy wrote: How large will the exponent be for a 10,000,000 digit prime number? digits x 3.32192 gives the approximate exponent. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: Distribution of Mersenne primes
For those of us who don't have access to Wagstaff's 1983 paper "Divisors of Mersenne Numbers", it is nicely summarized in "The New Book of Prime Number Records", by Paulo Ribenboim, chapter 6, section V.A. (page 411-413 in this edition). He gives 3 statements: (a) The number of Mersenne primes x is about log(log(x))*e^gamma/log(2) (b) the expected number of Mersenne primes between x and 2x is about e^gamma. (equivalent to part a) (c) the probability that Mq is prime is about c*log(aq)/q where c=e^gamma/log(2) and a=2 if q = 1 mod 4; a=6 if q=1 mod 4. It gives fours considerations upon which Wagstaff's conjecture is based. Of course, these imply that the nth Mersenne number is about [2^(-gamma)]^n, or 1.4759^n. He goes on to mention Eberhart's earlier conjecture of (3/2)^n, but states that there is no serious reason supporting this version of the conjecture. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Distribution of Mersenne primes
At 03:58 PM 6/26/99 -0400, Allan Menezes wrote: According to Paulo Ribenboim's book quoted below by Jud Euler's Constant gamma=0.577215665... and working out the number of mersenne primes below p=700 in Mathematica 4.0 gives 39.5572 primes, so we must be missing a prime if Wagstaffs' right. It doesn't work that way. It is a global property about the average number of Mersenne primes, so it doesn't say anything about a particular prime. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: this 3/2 conjecture and a result of Wagstaff
At 01:45 AM 6/24/99 -0700, Alan Simpson wrote:
It is clearly not the case that the exponent of the n-th Mersenne prime is
not (3/2)^P{n} or e^(gamma*n), but something like c^{n+o(n)), where "o(n)"
is the usual "little-o of n" (lim_{n \rightarrow \infty} o(n)/n = zero (a
severe abuse of notation in that limit!).
Do we have enough data to make any sensible guesses about the nature of this
"o(n)" term?
Not at this point. The data has always provided a very good fit to something
around 1.5. Here's the data:
N Best fit Correlation coefficient
2 1.5 1.
3 1.58114 0.9978
4 1.53252 0.9972
5 1.58263 0.9964
6 1.55430 0.9966
7 1.49068 0.9885
8 1.47602 0.9913
9 1.49766 0.9928
10 1.50665 0.9946
11 1.49615 0.9954
12 1.47691 0.9944
13 1.51560 0.9892
14 1.52890 0.9908
15 1.54999 0.9909
16 1.56791 0.9914
17 1.56752 0.9928
18 1.56434 0.9938
19 1.55793 0.9944
20 1.54433 0.9938
21 1.54132 0.9945
22 1.53166 0.9944
23 1.51928 0.9936
24 1.51220 0.9938
25 1.50214 0.9933
26 1.48995 0.9921
27 1.48331 0.9923
28 1.48093 0.9930
29 1.47755 0.9934
30 1.47278 0.9936
31 1.46983 0.9940
32 1.47466 0.9943
33 1.47661 0.9948
34 1.47817 0.9952
35 1.47747 0.9956
36 1.47932 0.9959
37 1.47850 0.9962
And another question, how does this linear curve (the term in the
exponential is linear in n, I mean) that people seem to want to attach to
the growth of the exponent of the n-th Mersenne prime change as n grows.
Could it be that if you look at the first 5 primes, and then the first 10
primes, etc., that the slopes are changing in some consistent manner?
See the above. For the known data, Wagstaff's estimate, exp(gamma*n), grows
progressively worse. (The ratio should be - 1.) Is there another constant
in the estimate I've omitted?
Of course, as the candidate exponents thin out, it may become accurate.
N Actual EstRatio
12 2 0.89
23 3 1.06
35 6 1.13
47 10 1.44
5 13 18 1.38
6 17 32 1.88
7 19 57 2.99
8 31 101 3.27
9 61 180 2.96
10 89 321 3.61
11 107 572 5.35
12 1271019 8.02
13 5211815 3.48
14 6073233 5.33
15 12795757 4.50
16 2203 10254 4.65
17 2281 18264 8.01
18 3217 32529 10.11
19 4253 57936 13.62
20 4423 103189 23.33
21 9689 183786 18.97
22 9941 327337 32.93
2311213 583010 51.99
2419937 1038384 52.08
2521701 1849437 85.22
2623209 3293981 141.93
2744497 5866818 131.85
288624310449228 121.16
29 11050318610831 168.42
30 13204933147238 251.02
31 21609159037631 273.21
32 756839 105150296 138.93
33 859433 187280292 217.91
34 1257787 333559763 265.20
35 1398269 594094094 424.88
36 2976221 1058124604 355.53
37 3021377 1884596547 623.75
+--+
| Jud "program first and think later" McCranie |
+--+
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Mersenne: safe to defrag?
Since Prime95 writes to the disk periodically, is it safe to do a disk defragmentation while it is running? +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: Mersenne exponent growth
There is a conjecture that the nth Mersenne exponent resulting in a prime is approximately (3/2)^n. Consider Mersenne primes through M37. (I don't know exactly what M38 is yet, and there may be other small ones. Also, the double checks of the range through M37 haven't been completed.) You can see the basis of this conjecture if you use semi-log graph paper and graph the index of the Mersenne exponents along the X axis and the exponents on the Y axis. If you don't have semi-log graph paper, graph the log of the exponent. (Or you can use software!) The data is pretty close to a straight line. If you do a linear regression of the log of the exponent vs. the index, you get a correlation coefficient of 0.996 - which indicates a very strong linear relationship. The linear regression parameters yield the relation M(n) = 1.4796^n + c, where c is a small constant. 1.4796 is pretty close to 3/2. This is one reason why we need to have a complete list of Mersenne primes up through some value. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Windoze joke
At 06:09 AM 6/14/99 -0400, [EMAIL PROTECTED] wrote: The reason it took so long is that it wasn't until now that ANYONE had Win9x run that long without rebooting. I might have actually hit that problem and not realized it. Until recently, for many months I had my old P-120 running in another room doing essentially nothing but Mersenne (double checks most recently). It was on a UPS, so unless there was a long-term power failure, it was on all of the time. I remember at least one time when it locked up for no apparent reason. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
No Subject
At 11:26 PM 6/13/99 -0600, Aaron Blosser wrote: This is supposed to be fun, and your behaviour makes it the oposite. I don't want to stand guard over my exponents, sending in false progress reports to make you stay away from them. Hey, whoa. I'm not asking anyone to send in false status reports. I *real* status report every now and then would do. In fact, a status report at least every 6 months seems quite prudent, don't you think? And personally, I think that if a test will take over a year to complete, you're probably better off doing factoring tests or double-checks, or maybe some other (integer based) distributed computing project altogether. I like GIMPS personally, but I'm not about to run Prime95 on my 486-75 laptop except maybe for factoring assignments. I know that factoring means you won't find the next record breaking prime, but so what? I try to run factoring assignments on my computers on the "recommended" 10:1 ratio... 1 factoring assignment for every 10 LL tests. Factoring is every bit as important to GIMPS as anything else. We're now doing first time LL tests in the 7M range...I can recall not too long ago when I would get factoring assignments in that same range, and I like knowing that I could use some of my slower machines to "pave the way" as it were. I'm not out to do all this just to get in the top-100 list...you could take away all my accumulated CPU time (though the others in my team madpoo might not like that) and that'd be fine because I'd still know that I'm contributing. Some people post to this list being upset that the work they turned in hasn't shown up in the primenet status lists yet. I know that this is a valid motivation for some people, but I do think they're missing a bigger picture. We have thousands of people all tied together into one huge, very well organized system. Scott and George have done wonders with putting this altogether. I merely suggest that we try to clean up some of the bits that ultimately will fall through the cracks. As I said before...exponents like the ones that were pointed out earlier are a very rare exception to the rule...but those exceptions must be dealt with to keep the coherency of GIMPS intact. But hey, this is just my opinion. After I test this little teeny tiny group of numbers, I won't poach anymore and you can all do whatever, but I still think it's a good idea to "clean house" every now and then. Aaron Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm X-Sender: [EMAIL PROTECTED] (Unverified) X-Mailer: QUALCOMM Windows Eudora Pro Version 4.1 Date: Mon, 14 Jun 1999 09:25:53 -0400 To: "Aaron Blosser" [EMAIL PROTECTED] From: Jud McCranie [EMAIL PROTECTED] Subject: RE: Mersenne: Re: Mersenne Digest V1 #575 Cc: "Mersenne@Base. Com" [EMAIL PROTECTED] In-Reply-To: [EMAIL PROTECTED] References: [EMAIL PROTECTED] Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" At 11:26 PM 6/13/99 -0600, Aaron Blosser wrote: +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: status of exponents
At 11:38 AM 6/13/99 +0200, Sturle Sunde wrote: And exactly how do you think that justifies that a GIMPS-participant does it knowingly? I'd like to ask the following of readers of this list who have been working on an exponent for more than 1 year, and have an expected completion date after 9/9/99. 1. What percentage of the computation has been completed? 2. What is the speed of the CPU? 3. How many hours per day is Prime95 actually running? +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: status of exponents
At 04:32 PM 6/13/99 +0200, Sturle Sunde wrote: Great. Next time Primenet tells me "Error, this exponent is already tested" on the exponent I reserved a few months ago, I should be very happy and tell myself: "Great! Someone have tested the exponent for me, and will get the credit if it was prime! I propose this as the honorable thing to do. First, you aren't likely to discover a prime, but if you do discover one that some other GIMPS person is working on, you should contact that person and share the credit. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
RE: Mersenne: status of exponents
At 09:32 AM 6/13/99 -0600, Aaron Blosser wrote: Criteria I used were: 1) Original *quite* long time to complete 2) No check-ins for a period of at least 6 months. I thought that if no check-in was done in 60 days, the number was put back in the pool. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: status of exponents
At 11:46 AM 6/13/99 -0500, Mikus Grinbergs wrote: To those on this list who are pursuing why certain exponents are not being completed "sooner" -- think about it -- WHAT DIFFERENCE WILL IT MAKE in __your__ life when exponent so-and-so is completed ?? I write the exponents resulting in primes down in my book, and I don't want to have to insert ones later. ;-) +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: status of exponents
At 04:32 PM 6/13/99 +0200, Sturle Sunde wrote: When a person tells the world which exponents he is testing, and continously reports his progress, people could at least complain to him before hijacking the exponents he has been testing for a year Some people that are out of contact may be using the buggy version 17, and their work is wasted. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: status pages
There seems to be a big discrepancy between what the status page at merseme.org shows (updated 6-6-99) and what the PrimeNet status page (updated hourly) shows as far as the exponents under 4,000,000. So maybe these small exponents that the former page shows that I was concerned about have actually been done. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
