Mersenne Digest Tuesday, October 19 1999 Volume 01 : Number 647 ---------------------------------------------------------------------- Date: Sun, 17 Oct 1999 02:16:42 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Mersenne: The Mysterious Ways of Mersenne primes On Sat, Oct 16, 1999 at 07:15:51AM +0300, Jukka Santala wrote: >(Personally, I don't believe there's any predictability to them) But then, they'd have to be randomly scattered around. To me, that idea seems a bit strange. These numbers are given a special property (being prime) by... randomness? My opionion is that there _is_ a relationship in most things (at least when it comes to something as `logical' and hard as primes), but it isn't always easy to find it :-) (Perhaps p will need some special property? Perhaps trying to continue a series isn't the way to go? Who knows?) /* 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: Sun, 17 Oct 1999 18:55:17 -0500 (CDT) From: Chris Caldwell <[EMAIL PROTECTED]> Subject: Re: Mersenne: The Mysterious Ways of Mersenne primes On Sun, 17 Oct 1999, Steinar H. Gunderson wrote: > On Sat, Oct 16, 1999 at 07:15:51AM +0300, Jukka Santala wrote: > >(Personally, I don't believe there's any predictability to them) > > But then, they'd have to be randomly scattered around. To me, that > idea seems a bit strange. These numbers are given a special We tend to be loose with the term "random," and in this case I think we mean "no easily determined pattern. E.g., "the primes are random." But that is not whay I decided to reply, rather I'd like to say I just realized a page I wrote which derives the Wagstaff conjecture can be found at http://www.utm.edu/research/primes/mersenne/heuristic.html I thought I had linked this in sometime ago--but I had not. This does not present Wagstaff's "derivation," but rather a more naive (or shall we say simplistic) approach that yields the same result. Chris Caldwell The Prime Pages _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 18 Oct 1999 14:44:47 +0200 (MET DST) From: Wojciech Florek <[EMAIL PROTECTED]> Subject: Mersenne: Milestone! Hi all! There should be the next milestone of GIMPS tomorrow (Oct 19) about 14:30 UTC. diamonddave should finish the double-checking of the last exponent below 2M (according to the PrimeNet Assignments Report). Regards and happy hunting! Wojciech Florek (WsF) email: [EMAIL PROTECTED] _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 18 Oct 1999 08:51:24 -0500 (CDT) From: Conrad Curry <[EMAIL PROTECTED]> Subject: Mersenne: P608 Factored P608 Factored NFSNET announces the complete factorization of P608 by the Special Number Field Sieve (SNFS). It was known that P608 = 641 * 14593 * 671233 * 6700417 * 620066693671553 * c149 where c149 is a 149 digit composite number given by c149 = 407212607938109927686391811109168199291928333967395\ 477888254196439811535677975754380014495465216898407\ 44351212863529579604939708442787844678618504833 On October 7, 1999 it was found that c149 = p62 * p86 where p62 = 729570376075162252904190636179938565056499153076206\ 90006389889 p87 = 558153978412300305901519135681489925326736859374781\ 699750217802894299569232242854570497 The factorization of P608 was 'Most Wanted' by the Cunningham project [1] which has the goal of factoring numbers of the form b^n +- 1 for b < 13. P608 was also the smallest number of the form 2^n+1 whose complete factorization was not yet known. The next smallest number of this form that has not yet been completely factored is P613. The sieving was done by a group of 32 volunteers. A total of 8.8M relations was collected forming a 1.294M x 1.296M matrix. The linear algebra and square-root phases were done at Centrum voor Wiskunde en Informatica (CWI) by Peter Montgomery. Acknowledgments are due to the volunteer sievers Pierre Abbat Sean Brockest Greg Childers Gary Clayton Conrad Curry Russell Dixon Geoffrey Faivre-Malloy Patrick Fossano Jeff Gilchrist Kelly Hall Philip Heede Jim Howell Don Leclair Joe Leherbauer Yaroslav Levchenko Chip Lynch Ernst Mayer Holger Menz Igors Mileika Thomas Noekleby Alexis Nunes Henrik Oluf Olsen Kirk Pearson Craig Renwick Anthony Rumpel Keith Schmidt Brian Schroeder Anastassios Sideridis simon Sturle Sunde Joe Williams David Willmore Special thanks to Bob Silverman, Peter Montgomery and Don Leclair. Also to CWI and the School of Mathematical Sciences at the University of Southern Mississippi for the use of their computers. NFSNET is currently sieving 10,184+, a 'Most Wanted' number, and 2,637+. If you would like to participate visit [2] and download the siever, your computer will need at least 10Mb of memory free. [1] http://www.cs.purdue.edu/homes/ssw/cun/index.html [2] http://orca.st.usm.edu/~cwcurry/nfs/nfs.html _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 18 Oct 1999 12:59:55 -0400 From: Jeff Woods <[EMAIL PROTECTED]> Subject: Re: Mersenne: Milestone! Won't happen on schedule. Look again: 1987523 D 60 1491838 109.4 1.0 61.0 18-Oct-99 15:54 01-Jul-99 06:03 diamonddave Ebi It has taken him from 1 Jul through now to get to 1.5MM iterations. He still has almost 500,000 iterations to go, a fourth of the number. While we don't know how long the assignment was made BEFORE he started checking the number, he has had it for 109 days. I doubt strongly that he'll finish on the 19th, as the estimate of time to run is likely wrong. But soon..... At 02:44 PM 10/18/99 +0200, you wrote: >Hi all! >There should be the next milestone of GIMPS tomorrow (Oct 19) about >14:30 UTC. diamonddave should finish the double-checking of the last >exponent below 2M (according to the PrimeNet Assignments Report). >Regards and happy hunting! > >Wojciech Florek (WsF) >email: [EMAIL PROTECTED] > > >_________________________________________________________________ >Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm >Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 18 Oct 1999 19:07:00 +0200 (MET DST) From: Wojciech Florek <[EMAIL PROTECTED]> Subject: Re: Mersenne: Milestone! On Mon, 18 Oct 1999, Jeff Woods wrote: > Won't happen on schedule. Look again: > [snip] > I doubt strongly that he'll > finish on the 19th, as the estimate of time to run is likely wrong. > > But soon..... > > I was observing the progress in the last 10 exponents below 2M. Almost all had been assigned to diamonddave and almost all have been finished on schedule ... Wojciech Florek (WsF) email: [EMAIL PROTECTED] _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 18 Oct 1999 14:32:38 -0400 From: George Woltman <[EMAIL PROTECTED]> Subject: Re: Mersenne: Milestone! Hi all, At 07:07 PM 10/18/99 +0200, Wojciech Florek wrote: >I was observing the progress in the last 10 exponents below 2M. Almost >all had been assigned to diamonddave and almost all have been finished >on schedule ... You missed one important step - the residues must match! I checked the cleared exponent report against the 3 remaining exponents below 2M. They have been completed and the residues match! The milestone was reached on October 16, at 12:09 UTC. Congratulations to all. Onwards and upwards, George P.S. It looks like diamonddave is working on an unneeded triple-check. Oh well, these things happen. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 18 Oct 1999 22:16:11 +0200 (CEST) From: Henrik Olsen <[EMAIL PROTECTED]> Subject: Re: Mersenne: Milestone! On Mon, 18 Oct 1999, George Woltman wrote: > Hi all, > > At 07:07 PM 10/18/99 +0200, Wojciech Florek wrote: > >I was observing the progress in the last 10 exponents below 2M. Almost > >all had been assigned to diamonddave and almost all have been finished > >on schedule ... > > You missed one important step - the residues must match! > > I checked the cleared exponent report against the 3 remaining exponents > below 2M. They have been completed and the residues match! The milestone > was reached on October 16, at 12:09 UTC. Congratulations to all. > > Onwards and upwards, > George > > P.S. It looks like diamonddave is working on an unneeded triple-check. > Oh well, these things happen. This seems to indicate he got poached, but he'd already started the doublecheck before the poacher sent in the result, so he's continuing with what has become a triple check. I noticed similar behaviour at the last exponents in the 1.4M range, where the last ones to finish got checked three or four times. - -- Henrik Olsen, Dawn Solutions I/S URL=http://www.iaeste.dk/~henrik/ I'd like somebody to sacrifice their first-borne son, and write in blood that gas does the right thing every time these days. Otherwise I will keep the thing that looks strange but has a real explanation for it. Linus Torvalds about buggy looking code that isn't _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 18 Oct 1999 18:17:23 -0400 From: George Woltman <[EMAIL PROTECTED]> Subject: Re: Mersenne: Milestone! Hi, At 10:16 PM 10/18/99 +0200, Henrik Olsen wrote: >> P.S. It looks like diamonddave is working on an unneeded triple-check. >> Oh well, these things happen. >This seems to indicate he got poached, but he'd already started the >doublecheck before the poacher sent in the result, so he's continuing >with what has become a triple check. I would not assume he was poached. More likely, the exponent had been assigned once, expired, and was reassigned to diamonddave. Later the original user sent in his result. There are other possible non-malicious reasons. Historically, poaching has been confined to the smallest *untested* exponents. At present, there seems to be little to no poaching going on. Regards, George _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 18 Oct 1999 23:48:35 EDT From: [EMAIL PROTECTED] Subject: Mersenne: Mmmm. Conjecturelicious. Hello again. <<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 believed for quite some time (and have proof that I did! :-P) that we are missing a Mersenne prime in there somewhere. However, I've only tried to improve on Wagstaff's conjecture, not fit a whole new line to the data. [Me:] <<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 >> [Someone else:] <<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.>> As someone pointed out, Wagstaff did not suggest 3/2, but 2^(1/e^gamma). By the way, if you note exactly how my graph and plot were constructed, y=x is correct to use. At least, I'm pretty sure so. (STL's taking a bold step here). Remember: by playing with the axes you can fiddle with slopes. <<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.>> I'm not sure if the r^2 would be affected by my choice of variables (which causes the y=x thing). <<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 saw that web page. The computations are not similar to mine in that the page explains Wagstaff's conjecture and why Erhardt was probably wrong, but I go further and point out how Wagstaff's conjecture often makes a wrong estimate for the Nth Mersenne prime, and present a new conjecture. <<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 just used a TI-92+ for the bulk of the work, and Mathematica 4.0 to make the plots/graphs for my paper. By the way, that paper for school is almost finished. I just have to write the conclusion and the abstract. Here's my conjecture, after I decided exactly which constant to use: M(x) ~ e^gamma log[2] x - 2^(1/e^gamma) S. "Figures that eventually he'll have to reveal his last name when he releases that paper" L. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 19 Oct 1999 00:28:52 -0500 From: Ken Kriesel <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: splitting up 10m digit primes How would you extend this concept to P-1, ECM, and factoring save files? Would revisions to the standard format be handled within the 8-byte Ascii file identifier, or in a separate field? Ken At 08:22 AM 1999/10/17 +0100, Nick Craig-Wood <[EMAIL PROTECTED]> wrote: >Some time ago I proposed a standard format for save files. It also >had the advantage that it only saved the actual bits used so would >make the save files 1MByte rather than 1.8 MByte for an 8,000,000 >exponent in prime95. (much omitted, see Nick's original post) _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 19 Oct 1999 00:53:32 -0500 From: Ken Kriesel <[EMAIL PROTECTED]> Subject: Re: Mersenne: Smallest unfactored composite (was types of work to request...) At 02:22 AM 1999/10/16 -0700, Greg Hewgill <[EMAIL PROTECTED]> wrote: >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 data becomes pretty sparse in bitmap format. With a little work we could do quite a bit better than that. First, the evens greater than two are known composite, so they need not have bits representing them. Second, the primes rapidly get sparse enough that it is more effective to record in several bits, the gaps between primes, or a multilevel lookup, than a simple yes-no table one bit per odd number. Third, if the usual data compression methods are more effective than such a table construct, we could use those compression methods. To answer Gordon Bower's question, very partially, Hans Riesel wrote (in Prime Numbers and Computer Methods for Factorization, 1985, Birkhauser) that in 1909 D N Lehmer published a factor table and prime table covering up to 10,017,000, and in 1959 C L Baker and F J Gruenberger published a table containing the first 6 million primes (all those below 104,395,289). And there have been a few posts if I recall correctly of how little time it takes on a modest speed computer to sieve up to 2^32 (~4,000,000,000+) http://www.utm.edu/research/primes/ contains a link to the Nth prime page at http://www.math.Princeton.EDU/~arbooker/nthprime.html "Enter 1 for the first prime (2), 2 for the second (3), on up to 1000000000000 for the trillionth prime (29,996,224,275,833)." So presumably the region that has been exhaustively searched for general primes is well above 3x10^13. Can someone else out there answer more precisely? 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? Ken _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 19 Oct 1999 07:49:32 +0100 From: Nick Craig-Wood <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: splitting up 10m digit primes On Tue, Oct 19, 1999 at 12:28:52AM -0500, Ken Kriesel wrote: > How would you extend this concept to P-1, ECM, and factoring save files? As far as I'm aware prime95 is the only program to do P-1, ECM or factoring so I wasn't intending that the save files should include these. Maybe they should? > Would revisions to the standard format be handled within the 8-byte > Ascii file identifier, or in a separate field? There was a 4 byte number for revisions at the start of the header. - -- Nick Craig-Wood [EMAIL PROTECTED] http://www.axis.demon.co.uk/ _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 19 Oct 1999 10:01:00 +0200 (MET DST) From: Wojciech Florek <[EMAIL PROTECTED]> Subject: 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!) If Noll's Island Theorem/Theory/Hypothesis is true then there are two of Mersenne primes in this region. Therefore, it is M40 below (???!!!???) or M41 (even more ! & ?) if M(6896873) is the the `upper' (north?) part of the island. Let's find them all -:) !!!! > M39: 6896873 (There is a prime at 6972593 in this region. But is it M38 or [snip] > - -*---*------- > S.T.L. Wojciech Florek (WsF) email: [EMAIL PROTECTED] _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 19 Oct 1999 14:15:31 -0400 From: George Woltman <[EMAIL PROTECTED]> Subject: Mersenne: Small exponents available Hi, You may have noticed a few hundred "small" exponents (4.5M - 8M) are now available at http://www.entropia.com/primenet/status.shtml I went through my log files and have requeued as a first-time LL test any exponent that had "serious" errors on the first LL test. A serious error is a "SUM(INPUTS) != SUM(OUTPUTS)" or "ROUNDOFF > 0.4". I'd guess that the first test has very roughly a 50% chance of being correct. I felt these exponents should be retested before the regular double-checking process gets up to that level. So if you get one of these small exponents, do not be surprised that the exponent appears in the already-tested list. Regards, George _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 19 Oct 1999 15:05:38 -0500 From: Ken Kriesel <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: splitting up 10m digit primes At 07:49 AM 1999/10/19 +0100, Nick Craig-Wood <[EMAIL PROTECTED]> wrote: >On Tue, Oct 19, 1999 at 12:28:52AM -0500, Ken Kriesel wrote: >> How would you extend this concept to P-1, ECM, and factoring save files? > >As far as I'm aware prime95 is the only program to do P-1, ECM or >factoring so I wasn't intending that the save files should include >these. Maybe they should? Surely there are other programs. There must be various factoring efforts running on non-Intel processors under non-Microsoft operating systems. >> Would revisions to the standard format be handled within the 8-byte >> Ascii file identifier, or in a separate field? > >There was a 4 byte number for revisions at the start of the header. I took the 4-byte number present in your first recent post to be the version information of the program that generated the file, not the file standard version. After rereading Brian's comments and your reply to him, I think I get it; Brian's modification adds the program version levels, and the original had the standard's version. (Feeling fuzzy from the flu, please pardon the increased noise level.) Ken _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 19 Oct 1999 01:01:07 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Mersenne: Re: The Mysterious Ways of Mersenne primes On Tue, Oct 19, 1999 at 01:55:32AM +0300, Jukka Tapani Santala wrote: >you can compare this to something like the value of Pi, relation of the >radius to the circumference, which human mind tries to instantly >rationalize as a "real" number, demonstrated clearly by the actual attempt >to _legalize_ Pi as 3. In fact, ask anyone what Pi is, and majority of >them will instantly reply to you "3.14". I'd say 3.1415926535897932, just to confuse people :-) (Yes, I do remember those decimals. Why? For fun.) A friend of mine, being really tired at a LAN-party, decided we should get away with our 10-system, and start using a phi-system instead. Sounds good in theory, but then you suddenly can't get to know exactly how many fingers you've got either? >The square of two is another good >example of how "irrational" and counter-intuitive mathemathics really is. You made a slight typo there -- you did mean the square _root_ of two, did you? >To really claim that primes are either "random" or "non-random" >in nature would give you a ranom chance of being right ;) But then, define random! If I toss a (`fair') coin, I'd say that it's random. However, a very quick viewer (or a computer) might see the moment before the coin hits the ground (and stays there), what it will turn up as. In other words, then the randomness is _not present_ at that time. Now, if you go backwards, you can probably calculate (if you're VERY quick -- remember this is all theoretical) this earlier on, perhaps all the way back to when the coin leaves your hand. Who knows, perhaps even further? :-) /* 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 ------------------------------ End of Mersenne Digest V1 #647 ******************************
