Re: Mersenne: M39 Text
At 10:39 AM 12/10/01 -0500, [EMAIL PROTECTED] wrote: I tried getting the M39 text file from the Mersenne site, but it keeps saying it is unavailable. Was it taken offline because of heavy traffic? Randy Given [EMAIL PROTECTED] (forwarded) FYI: The digits of the 39th known Mersenne prime: http://www.mersenne.org/13466917.htm are available: http://www.isthe.com/chongo/tech/math/prime/mersenne.html#largest In particular: Decimal diigits: http://www.isthe.com/largest.known/prime-c.html English name: http://www.isthe.com/largest.known/prime-d.html without -'s: http://www.isthe.com/largest.known/prime.html chongo (Landon Curt Noll) /\oo/\ _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
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
Re: Mersenne: Factor of 2^(2^31-1)-1 found ($)
On Sun, 19 Sep 1999, Lucas Wiman wrote: All (and especially Chris), Yesterday (and the day before), I went to the Illinois number theory conference. There (2nd talk of yesterday) J. P. Selfridge announced that he would give away $1000 US for any factor found of a number which ought to be prime (he provided a list). On that list was 2^(2^31-1)-1. I will check with him on what he meant--I notice at least one other number on his list is already factored. I will post the revised list here as soon as I get it. Chris _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: A possible venue for a GIMPS meeting
One of these lists: Primes-L or Mersenne, had mentioned having folks get together at a number theory meeting. The third of these below might be the ideal time--if folks were still interested we could contact the organizors and arrange a session (I would be willing to). For example, depending on interest, we could try to arrange talks on the history of primes and Mersenne finding, or a panel discussion of GIMPS/PrimeNets/Proth's future, papers on the basic heuristics of prime searching... Since Primes-L/GIMPS both include folks at all levels of math, there is room for a very wide variety of presentations. It would be fun to organize these session(s). = The University of Illinois at Urbana-Champaign is having a "Special Year in Number Theory 1999/2000" which involves having a number of long term visitors, and several meetings: (See http://www.math.uiuc.edu/nt2000/ ) Illinois Number Theory Conference, September 17-18, 1999 "One hour talks will be given by K. Alladi, P. Borwein, A. Pollington, and K.S. Williams. There will be opportunity for about 20 contributed talks." No registration fee. Midwest Arithmetical Geometry in Cryptography Workshop, November 5 - 7, 1999 "This workshop is intended for people in academia and industry with a basic mathematical background in group theory and number theory, wishing to learn about the increasingly common applications of arithmetical geometry to cryptography. The featured speakers are Neal Koblitz, Joe Silverman, and Nigel Smart, each of whom will give three hour talks. There will also be time for contributed talks." (This one:) *** Millennial Conference on Number Theory, May 21 - 26, 2000 "Confirmed plenary speakers include G. Andrews, J. Coates, H. Darmon, K. Ford, R. Graham, A. Granville, D.R. Heath-Brown, C. Hooley, W.-C. Li, K. Murty, M. Nathanson, K. Ono, C. Pomerance, W. Schmidt, C. Skinner, K. Soundararajan, R. Taylor, R. Tijdeman, and R.C. Vaughan. Several of the plenary talks will be in the form of broadly accessible survey lectures. Proceedings will be published." AMS Sectional Meeting at Urbana, March 18 - 21, 1999 "We expect that around 70 talks at this meeting will be in number theory." Instructional Conference on Fermat's Last Theorem, Summer 2000 === Postscript: "Good" number theory meetings are relatively common, but this "Millennial Conference" looks like it will be exceptional. The list of speakers is already very impressive and they will have "broadly accessible survey lectures" (though that couuld mean many things...) Because of that, it may be worth folks going to the expense to come. What do you think? Should we try to organize something? Chris Caldwell _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: More on the FAQ
On Thu, 1 Jul 1999, Lucas Wiman wrote: All, I've done a bit more work on the FAQ, I added the two responses I'd strongly suggest using the strength of the web and connecting many of the answers to the fuller explanations already on the web. E.g., those you mention using (or planing to use) below without reference in your draft. (I assume you'll do this eventually, but sometimes it is easier to collect references while drafting.) of mersenne primes. I don't know if section 5 will ever get written, or if it needs to be. If it does get written it probably won't be by me, since I don't know enough about such things. I think that with the aid of Luke's and Chris Caldwell's sites I should be able to do this pretty easily. For the distribution of primes see the new page http://www.utm.edu/research/primes/notes/faq/NextMersenne.html which briefly discusses the Wagstaff/Lenstra/Pomerance e^gamma conjecture. Chris Caldwell Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Basic question: Working modulo 2^n-1
On Fri, 15 Jan 1999, Foghorn Leghorn wrote: Chris Caldwell's web page on Mersenne numbers descirbes the Lucas-Lehmer test briefly and mentions that it is quick on binary computers because they can quickly perform division by 2^n-1. I know how to find integer quotients and remainders modulo 2^n with shifting and masking, but I don't understand how it is done quickly modulo 2^n-1. Would anyone care to explain? The remark was indended to refer to the classical algorithms (with the right choice of FFT algorithm this step is automatic): the key is that 2^n = 1 (mod 2^n-1), so if we write the number as A*2^n + B (that is, let B be the last n bits and A the rest, then A*2^n+B = A+B (mod 2^n-1). So we can reduce with just an addition. For exampe, take the number 23 modulo 7, 23 is (mod 7) 10111 = 10 + 111 = 1001 = 1 + 001 = 10 (mod 111) Chris.
