Re: Mersenne: Smallest unfactored composite (was types of work to request...)
On Fri, Oct 15, 1999 at 01:03:57AM -0800, Gordon Bower wrote: PS - On an unrelated note --- what is the smallest natural number that is not known whether it is prime or composite? Surely *someone* out there is trying to work from the bottom up and factor every number. (I don't know the answer. I am guessing the it is a smallish number of maybe 15 or so decimal digits?) Suppose you were keeping such a list. With one bit (prime vs not-prime) to represent each number up to 10^15, you would need approximately 10^14 bytes of storage, which is on the order of 100 terabytes. That would be your first problem. The second problem would be if you were to present me with the smallest number that was not factored, I could almost immediately present you with a factorization (or show that it's prime). The point is there are so many numbers, it would take far too much time to determine the character of even the small ones that could individually be characterized almost immediately. Here's another argument - suppose the largest unfactored composite was C. How long did it take to determine the factorization (or primality) of C-2? (C-1 would be even.) Then to factor C would only take a marginally longer amount of time than it took for C-2. There is no reason you could not complete the factorization of C. Greg Hewgill _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Smallest unfactored composite (was types of work to request...)
On Fri, Oct 15, 1999 at 01:03:57AM -0800, Gordon Bower wrote: Here's another argument - suppose the largest unfactored composite was C. How long did it take to determine the factorization (or primality) of C-2? (C-1 would be even.) Then to factor C would only take a marginally longer amount of time than it took for C-2. There is no reason you could not complete the factorization of C. Alas, if Gordon's argument is valid, then every positive integer would be factored. This is the principle of mathematical induction. A computer may be in a loop. It has factored C-2 and C-1, and is now working on C. The task of factoring C may indeed take only marginally longer than it took for C-2, but the extra time is nonetheless positive. The next number may be factored as you read this paragraph, so a journal article saying "Every number below this C has been factored, but C itself has not been" would become outdated almost immediately, even if true when submitted. We can use the same argument on how much water our bodies will hold, or how much pollution to allow. At any given time, adding a single molecule may seem safe. But the capacities are finite. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: splitting up 10m digit primes
On Sat, 16 Oct 1999, Jukka Santala wrote: "Brian J. Beesley" wrote: On 14 Oct 99, at 18:15, Chris Jefferson wrote: Surely this isn't really an issue. PrimeNet would surely recognise a result submitted by a "poacher" as such either disqualify it automatically, or credit the actual owner of the assignment instead of the "poacher". Except that PrimeNet doesn't control the prize. This is the error everybody is doing. EFF is adminstrating the competition and prize, given by anonymous donaters to advance distributed computing / mathemathical algorithms on computers. PrimeNet is just one of the organizations (With largest changes known!) to get that prize, but it doesn't decide upon who gets it. The first person to present a prime filling the requirements will - and that's why result-files "few iterations short" will be worth more than their weight in gold. Yes, but the licence for Prim95/NT specifies that anyone who uses this program must obey it's licence. Someone using a partly completed file would also be liable under this. However, proving that they has used the interim file generated by this particular program might be difficult... _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: splitting up 10m digit primes
On 16 Oct 99, at 7:35, Jukka Santala wrote: [ ... snip ... ] Except that PrimeNet doesn't control the prize. This is the error everybody is doing. EFF is adminstrating the competition and prize, given by anonymous donaters to advance distributed computing / mathemathical algorithms on computers. PrimeNet is just one of the organizations (With largest changes known!) to get that prize, but it doesn't decide upon who gets it. The first person to present a prime filling the requirements will - and that's why result-files "few iterations short" will be worth more than their weight in gold. I think, if someone tried to pull this particular stunt, PrimeNet could inform EFF of the claimant's theft of the right to the discovery (which is what it amounts to). Another unfortunate example of the way in which large ca$h prizes can lead to unpleasantries, I'm afraid. You said... about making the repository write-only. And you seem to completely miss the point; the discussion here has centered around how to solve the problem that PrimeNet doesn't have the bandwidth or storage space to backup the intermediary files! So my suggestion was "distributed storage". This will solve the backup problem, but yes the above-mentioned prize-claim and double-check problem remains. Unfortunately, I think in that respect we're stuck. Well, I sort of _did_ miss that particular point. But I have a solution. If you have a distributed filestore, controlled by a number of different people, then you encrypt hack up the file you're saving and scatter pieces amongst the remote filestores. If you (the assignment owner) use a method based on a key otherwise known only to PrimeNet to scramble scatter the file, the small chunk of data stored on any other individual's system is useless to them for the purposes of hijacking your work. I think PrimeNet should know users' keys so that data can be recovered in the event of the user defaulting or accidentally destroying their own key (so that work done isn't lost). Presumably we trust the people running PrimeNet! An obvious extension to this idea is to use a RAID type technique e.g. if you store each bit of a byte on a seperate host, so that the file is scattered over 8 hosts, you could send the parity bit to a ninth host. Then the distributed filestore is immune to loss of one of its hosts (by reason of network failure or unsecured loss of its filestore). As for bandwidth and total filestore space needed - the first is, and will probably remain for some time, a problem, at least for most home users. 10,000 x 8 Mbyte save files is a lot of data by today's standards; nevertheless, 4 20GB drives at $200 each would just about cover it. (A random dip into a UK magazine shows Samsung 20.3GB UDMA66 IDE at £144 (sterling) each, so US$10 per GB should be achievable) 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: Islands of Truth
On Fri, 15 Oct 1999, Jud McCranie wrote: At 05:45 PM 10/15/99 -0400, you wrote: I've put a graph of these "pairs" up on my web page. You can't really tell much from that graph - most of the points are hugging the x-axis. Most of those are pretty random... like, the higher your numbers get, the more grouped they are. I have more thoughts on this, from reading http://www.utm.edu/research/primes/notes/faq/NextMersenne.html a few times, but I gotta get going. __ PGP fingerprint = 03 5B 9B A0 16 33 91 2F A5 77 BC EE 43 71 98 D4 [EMAIL PROTECTED] / http://www.op.net/~darxus Join the Great Internet Mersenne Prime Search http://www.mersenne.org/prime.htm _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: The Mysterious Ways of S.T.L.
"Brian J. Beesley" wrote: They will, and they're very likely to be artificial. Umm. I'm moderately familiar with statistics, that's actually part of why I'm not looking for significance in the patterns. (For one thing, the wole concept of statistics kinda excludes the possibility of using it to "find the right one", like some people seem to be assuming they can do. Kinda like the various countries hosting a celebration for the birth of the 6 billionth person on Earth;) However, I was suggesting to those actually looking for patterns in there not to automatically assume they need to work with the set of all Mersenne exponents vs. exponents of prime Mersennes. For one thing, this will very rarely yield a result that is even a candidate (As some have found out). On the other hand, this could be a way to check the working of the conjencture... We can artificially generate this situation, thouhg. However, small correction: With Mersennes, the Mersenne numbers size is directly propotional to the exponent or number of bits in the number, so obiviously there's not much sense in testing the two separately ;) -Donwulff _ 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
On Fri, 15 Oct 1999, John R Pierce wrote: Darxus wrote: I've put a graph of these "pairs" up on my web page. http://www.op.net/~darxus/p_pairs.bmp Never use BMP on the WWW, please! There's no way for me to look at that. Interesting, what browser are you using ? here, I whacked it for you... http://hogranch.com/files/Bitmaps/p_pairs.gif since it was a very-few color chart, GIF was the logical format. BMP was 71k. GIF is 4K. nuff said? I do not like .bmp because of microsoft and the fact that Jukka can't view it (whatever the reason is). I do not like .gif because of the copyright/patent thing on its compression. As far as I'm concerned, that only leaves .png, who's support is lacking. Unfortunately, at this moment, I do not have the ability to do any conversions, so thank you for putting up a .gif. __ PGP fingerprint = 03 5B 9B A0 16 33 91 2F A5 77 BC EE 43 71 98 D4 [EMAIL PROTECTED] / http://www.op.net/~darxus Join the Great Internet Mersenne Prime Search http://www.mersenne.org/prime.htm _ 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
On Sat, 16 Oct 1999, Darxus wrote: On Fri, 15 Oct 1999, Jud McCranie wrote: At 05:45 PM 10/15/99 -0400, you wrote: I've put a graph of these "pairs" up on my web page. You can't really tell much from that graph - most of the points are hugging the x-axis. Most of those are pretty random... like, the higher your numbers get, the more grouped they are. I have more thoughts on this, from reading http://www.utm.edu/research/primes/notes/faq/NextMersenne.html a few times, but I gotta get going. Okay, that page is a bit overwhelming for me, but it looks like it's saying that, when you graph log(log(p)) vs. n, where the logs are base 2, p is part of 2^p-1, and n is the number of the mersenne prime (did I say that right?), you'll get an approximation of a straight line. All mersenne primes will fit that pattern, but they are less likely to be *on* the line than they are to be *near* the line. Geez, I'm having difficulty putting this into words. Like... primes are not likely to fall extreemly close to the line, but they're probably going to be near it -- like, they're magnetically repelled from the line. This would cause random clumping. It would also cause random clumping when you graph P vs. N (where P is part of 2^P-1, and N is the number of the merseene prime). I have no idea what would cause this, but if it's correct, we should be able to calculate the probability of the distance from the line (if you're doing the log log thing, or if you're fitting an exponential curve), and predict more accurately where a prime would fall (you'd be predicting 2 points, one on either side of the line). Gonna go regression test (proper term?) the extrapolations I've been playing with assuming the distribution is totally random but approximating an exponential curve __ PGP fingerprint = 03 5B 9B A0 16 33 91 2F A5 77 BC EE 43 71 98 D4 [EMAIL PROTECTED] / http://www.op.net/~darxus Join the Great Internet Mersenne Prime Search http://www.mersenne.org/prime.htm _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne Digest V1 #645
Mersenne Digest Saturday, October 16 1999 Volume 01 : Number 645 -- Date: Fri, 15 Oct 1999 20:03:02 +0100 From: "Brian J. Beesley" [EMAIL PROTECTED] Subject: Re: Mersenne: Modular arthimatic.. On 15 Oct 99, at 18:25, Chris Jefferson wrote: Just something I was pondering a couple of days ago... 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... Ways of doing this: The difference of two squares is always an arthimetic progression of odd numbers. Here is an example.. 2^2 - 1^2 = 3 3^2 - 2^2 = 5 4^2 - 3^2 = 7 and so on... So look at general sum of an arthimetic series S(n) = (n/2)(2a + (n-1)d) In this case d=2 and a is odd, so need to try to solve c = na + n(n-1)/2 for integers n,a Also, try to solve x^2 - y^2 = 0 mod c Are we not back to Fermat's Method for factorization (again)? If we're dead lucky and pick a value c such that a and b are very similar in magnitude, this method works a treat (hence it's very unwise to pick a public key which factorizes into two nearly equal numbers. You make the job of cracking your key a lot harder if you pick the product of two numbers which differ in length by a couple of bits.) There is still a gap between the largest factors which can be found (practically, not theoretically) by techniques suited to "small" factors, like trial factoring, P-1 and even ECM, and Fermat's Method which is practical only for "small" values of b-a. (Fermat is just plain _awful_ at factorizing 3*p for large prime p!) Probably the continued fractions method is the best line of attack on numbers which resist "reasonable" efforts with other methods. Regards Brian Beesley _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers -- Date: Fri, 15 Oct 1999 21:34:02 +0200 From: "Steinar H. Gunderson" [EMAIL PROTECTED] Subject: Mersenne: Re: splitting up 10m digit primes On Thu, Oct 14, 1999 at 06:15:52PM +0100, Chris Jefferson wrote: In my personal opinion, the best way of doing this would be to set up 3 computers in a 'loop' all doing the same exponent. Then they could communicate at regular intervals. We are already doing this manually, although only with 2 computers (if the residues match, you don't need the 3rd one). We're taking residues every one million iterations, and mail them to each other. So far, they've matched :-) And if one machine is faster than the other -- well, then it goes on to another exponent. No waiting needed. /* Steinar */ - -- Homepage: http://members.xoom.com/sneeze/ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers -- Date: Fri, 15 Oct 1999 17:10:58 EDT From: [EMAIL PROTECTED] Subject: Mersenne: The Mysterious Ways of S.T.L. Hello, everybody. As usual I'm quoting different people. Disturbingly, I noticed a weird HTML tag on my last E-mail. I can assure you I didn't put it there, and don't know why my software's acting up on me (because I've never seen that jibberish before). HTML mail is evil, only second to MIME. Long live ASCII! Please excuse my delay in sending this message. Also, if this extrapolation of the number of digits is accurate, there is another prime between the 37th 38th(p=6972593) discovered primes. Unfortunately, the extrapolation of P just didn't go well. Actually, the extrapolated 39th mersenne prime is 6.34% off of 2^6972593-2. I suppose that's not so bad. That would also mean one was skipped. So it is currently my fairly strong opinion that a mersenne prime was skipped between the 37th 38th discovered primes. I reserve the right to change my mind at any instant. I'd also guess that the skipped prime may have been pretty close to 2^5014947-1, and have a number of digits close to 1408773. This is similar to the conjecture I made oh-so-long ago. 6.9M was confirmed, but at the same time I had to predict a missing one (which I said was probably in the 4M range, but that's far less certain). [EMAIL PROTECTED]: I'm really looking forward to hearing how you made your estimates. How did you make this estimate ? Fit an exponential curve to the known primes, and extrapolate the 1st one that should have at least 1m digits? Who knows the mysterious ways of STL? I usually just go by S.T.L. (my initials). At some point I had a vague recollection that STL had believed there was a number missing, and I was quite happy to see that
Re: Mersenne: problem with prme95 - spl file - ME TOO !
Brian, This will probably make you laugh, if it does don't tell me, I was not ammused when I found out what had happened, read on... On 15 Oct 99, at 13:16, Michael Oates wrote: I am also having the same problem, but only on one machine, I have 9 others that are fine, all are using the same version of v19 beta 4 What's different? Must be _something_ ... I have been running Prime95 on this machine for about 4 weeks. It is on a LAN with other machines also running Prime95. I have a shortcut to run the program in the Startup folder. Today I realised that not only was the server not being updated, but the save files had not been altered for over a week. This was very odd as the program was re-starting correctly where it left off. So I thought, it must be storing the save file somewhere else. Then I also noticed that some of the setting details were wrong, not just wrong, but were for a different machine. I ran the program from the directory with File Explorer and it used a different exponent and was at a different stage ! Eh !!! I checked the shortcut that was in the Startup folder... well would you believe it... it was pointing to another machine. Some how Windows95 had changed the path to the shortcut all on it's own, and had been running another exponent on another machine over the network. And for some odd reason the details stored in local.ini were taken from the local machine and the details from prime.ini were from the remote. Now I know what you are probably thinking, it was not Windows95 that changed the path, and that I made a mistake when I set it up... WRONG, very wrong. I have seen this before... if you have a shortcut to a file, and remove the file, and replace it with another one Windows95 inserts another path in any shortcut to that program, this has cause no end of problems in the past. This probably happend when I upgraded Prime95 with a newer verion, I moved the directory else where by mistake, instead of copying it to make a backup. I of course just copied it back again straight away, then copied the new updated program to it... from... wait for it... the machine that the new shortcut was pointing to. So somehow windows changed the shortcut path to the directory on the remote machine, great eh ! All is now working ok, but I have lost over a weeks LL testing because of it. No harm seems to have been done to the remote machine. Regards, Mike, -- ATLAS CELESTE - Bevis Star Atlas - "The CD-ROM" A very rare atlas found at the Godlee Observatory http://www.u-net.com/ph/mas/bevis/ Astronomy in the UKhttp://www.ph.u-net.com _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: problem with prme95 - spl file - ME TOO !
On Sat, 16 Oct 1999, Michael Oates wrote: I have been running Prime95 on this machine for about 4 weeks. It is on a LAN with other machines also running Prime95. I have a shortcut to run the program in the Startup folder. For Windows 95 and prime95, this is the wrong approach, since as the included story shows, this makes you vulnerable to the mangling of shortcuts that Windows loves and we hate. Instead, remove the shortcut from the startup folder, start prime95 manually, choose "Options" and make sure "Windows 98/95 Service" is checked, then it will start automagically, this is especially important in networked setups, as the service runs even when noone's logged in. Today I realised that not only was the server not being updated, but the save files had not been altered for over a week. This was very odd as the program was re-starting correctly where it left off. So I thought, it must be storing the save file somewhere else. Then I also noticed that some of the setting details were wrong, not just wrong, but were for a different machine. I ran the program from the directory with File Explorer and it used a different exponent and was at a different stage ! Eh !!! I checked the shortcut that was in the Startup folder... well would you believe it... it was pointing to another machine. Some how Windows95 had changed the path to the shortcut all on it's own, and had been running another exponent on another machine over the network. And for some odd reason the details stored in local.ini were taken from the local machine and the details from prime.ini were from the remote. Now I know what you are probably thinking, it was not Windows95 that changed the path, and that I made a mistake when I set it up... WRONG, very wrong. I have seen this before... if you have a shortcut to a file, and remove the file, and replace it with another one Windows95 inserts another path in any shortcut to that program, this has cause no end of problems in the past. This probably happend when I upgraded Prime95 with a newer verion, I moved the directory else where by mistake, instead of copying it to make a backup. I of course just copied it back again straight away, then copied the new updated program to it... from... wait for it... the machine that the new shortcut was pointing to. So somehow windows changed the shortcut path to the directory on the remote machine, great eh ! All is now working ok, but I have lost over a weeks LL testing because of it. No harm seems to have been done to the remote machine. Regards, Mike, -- ATLAS CELESTE - Bevis Star Atlas - "The CD-ROM" A very rare atlas found at the Godlee Observatory http://www.u-net.com/ph/mas/bevis/ Astronomy in the UKhttp://www.ph.u-net.com _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers -- Henrik Olsen, Dawn Solutions I/S URL=http://www.iaeste.dk/~henrik/ Catherine: Go to hell! Gabriel: Heaven, heaven. At least get the zip code right. The Prophecy _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Bold Predictions From STL's Mysterious Ways
(I'm quite poor at choosing subjects, you see.) Well, I found my notecard of predictions that I had calculated a while ago with my conjecture. Here are some of the values I computed. These can either be used for a good laugh (M100 in particular is nice to look at), or you can write these values down and see how close they hit the mark (live long and find Mersennes?). At the time I only had data for Mersenne prime exponents up to 3021377 (i.e. not 6972593), and I calculated what M37 should have been as a test. It's pretty close. My prediction for the 6M prime was also close. Now, to find the missing Mersenne Here I call M# to be q instead of 2^q-1 for brevity. M37 (known at the time to actually be 3021377): 3166795 M38: 4673434 (the elusive missing Mersenne?!? If there is no Mersenne prime around here, then the 3021377-6972593 gap is almost as large as the 127-521 gap!) M39: 6896873 (There is a prime at 6972593 in this region. But is it M38 or M39?) M40: 10178139 M41: 15020505 M42: 22166682 M43: 32712733 M44: 48276189 (hence my conjecture that the decamegaprime is either right at the 10M digit limit, or has an exponent around 48M) M50: 498689073 M75: 8379797036294 M100 ~ 14081118310500 (that's its EXPONENT, whoo hoo. The inaccuracy is due to the precision limitations of my calculator) As for myself, I'm *really* hoping that there's a missing Mersenne. Time will tell -*---*--- S.T.L. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: AMD K6 and Athlon
On Sat, Oct 16, 1999 at 03:47:42PM -0400, Jud McCranie wrote: I tried version 19 on a PII and a Celeron, and in both cases it thought they were P-Pros. It got the MHz correct. Were these upgraded, or fresh installs? The GIMPS software (still no collective name for Prime95/Saver95/mprime/ntprime?) won't try a redetection if there already is a CPU type entry available. /* Steinar */ -- Homepage: http://members.xoom.com/sneeze/ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: Reliability (was Re: splitting up 10m digit primes) + Possible Wish List item
On Sat, Oct 16, 1999 at 06:27:24AM +0300, Jukka Santala wrote: If you can afford the bandwidth and storage space, you can check the box. The problem probably doesn't lie at the user's end. The server is the one with the storage problem, and probably the one with the bandwidth problem as well... /* Steinar */ -- Homepage: http://members.xoom.com/sneeze/ _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Bold Predictions From STL's Mysterious Ways
STL: what was the line you fit to the log log of the known mersenne's exponents, and what was the error (r^2) ? I'm assuming r^2 is like, the amount of error for a given line fitting a set of data. When I fit an exponential line to the 1st 37 mersenne prime's exponents (since I believe that 6972593 is actually the 39th, but have no proof, so I figured I'd leave it out), the line I got was y=1.7661e^0.301x (hope I wrote that right), and r^2=0.9925. I have a feeling the log log thing will actually be more useful.. easier to predict a straight line than an exponential curve. __ PGP fingerprint = 03 5B 9B A0 16 33 91 2F A5 77 BC EE 43 71 98 D4 [EMAIL PROTECTED] / http://www.op.net/~darxus Join the Great Internet Mersenne Prime Search http://www.mersenne.org/prime.htm _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Re: AMD K6 and Athlon
Hi, At 02:22 AM 10/17/99 +0200, Steinar H. Gunderson wrote: On Sat, Oct 16, 1999 at 03:47:42PM -0400, Jud McCranie wrote: I tried version 19 on a PII and a Celeron, and in both cases it thought they were P-Pros. It got the MHz correct. Were these upgraded, or fresh installs? The GIMPS software (still no collective name for Prime95/Saver95/mprime/ntprime?) won't try a redetection if there already is a CPU type entry available. Prime95 does not detect Celerons very well. However, if a PIII, PII or Celeron is detected as a Pentium Pro - its no big deal. All those CPU types use the same code. Regards, George _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: The Mysterious Ways of S.T.L.
On Fri, 15 Oct 1999 [EMAIL PROTECTED] wrote: Then, I plotted e^gamma log[2] (mersenne) versus the list of 1-37. Alongside this I graphed y=x. This is because the y=x line represents the Wagstaff y=x would be a slope of 1/1. According to the "Where is the next larger Mersenne prime?" page -- http://www.utm.edu/research/primes/notes/faq/NextMersenne.html the Wagstaff conjecture suggests a slope of 3/2, which I believe wouldn't look so bad. So, I graphed e^gamma log [2] (mersenne) - (1, 2, 3, 4, etc). This represents how far off the Wagstaff conjecture is when applied to the data. (The Wagstaff conjecture *should* say that M(3021377) = 37, but it doesn't. This is why I graph this jibberish). This graph was INCREDIBLY disturbing. Save for one Mersenne prime, all these "errors" were above 0, and often big. Ech! So, I used my TI-92+ to take a linear regession line of this data (because I had recently learned how to do regression lines and correlation coefficients). This line was Y = .004769x + 1.4615. See what's happening here? It seems that there's a consistent error (1.4615) in the Wagstaff conjecture that doesn't change as the Mersenne primes grow (the .004769). So I went back and applied this correction to the graph "that seemed a little strange" and it fit y=x much better. Sorry it didn't register to me that you'd mentioned the equation for this line in this post, thanks. But what was r^2 for it ? I'm very curious. On the previously mentioned web page, there are similar computations, but I believe he used M38 (which you and I believe will actually turn out to be M39), so I believe his numbers will be less accurate than yours. I would really like to try your calculations myself, but I haven't seen my graphing calculator for a while, I'm not sure it'd work, and I'd prefer to use the power of my computer. Can anybody suggest any programs ? Preferably for Linux, even though that would mean I'd have to wait to get my Linux drive back. I am most anxious to take M1-M36 extrapolate M37, down through having just, say, M1-M10 extrapolating M11 see how accurate that process is. I really thing the GIMPS client should have an option to test the mersenne number closest to this estimate of M38 that has not been and is not being tested -- implemented in a scalable fasion, so that when/if the missing prime is found, and it finishes the number it's on (since knowing what isn't prime is valuble), it'll then go to the next estimated prime. __ PGP fingerprint = 03 5B 9B A0 16 33 91 2F A5 77 BC EE 43 71 98 D4 [EMAIL PROTECTED] / http://www.op.net/~darxus Join the Great Internet Mersenne Prime Search http://www.mersenne.org/prime.htm _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
