20120416, 15:07  #1 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
Bernoulli(200) c204
Hi all,
Barry Mazur and William Stein have inquired whether it were possible to obtain the factorization of the numerator of the 200th Bernoulli number. The factors 389, 691, and 5370056528687 are known, leaving a c204: Code:
N = 345269032939215803146410928173696740406844815684239672101299206421451944591925694154456527606766236010874972724155570842527652727868776362959519620872735612200601036506871681124610986596878180738901486527 A c204 is a factorization with chest hair, but I think RSALS could handle it. Would you be interested in this? Can someone take on the matrix? 
20120416, 15:13  #2 
(loop (#_fork))
Feb 2006
Cambridge, England
3^{3}·239 Posts 
I don't believe RSALS can handle it, they're only geared up to use the 14e siever. This sounds like a good candidate for nfs@home, and they have the right sievers for it, but I think they're busy.
Order of a CPUcentury to sieve and therefore a CPUdecade to do the polynomial selection (so a season on my 48Opteron machine). I could do the matrix, it would take me about a season on 24 Opteron cores, but I suspect frmky has grids that could do it faster. How much ECM has been done on the cofactor? I think this may well be too hairy a problem to be reasonable with what we've got here now; I'm not really prepared to commit two seasons (so the thick end of a thousand dollars in depreciation and electricity) for an aside even in a book by Mazur and Stein Last fiddled with by fivemack on 20120416 at 15:17 
20120416, 15:15  #3 
"Nancy"
Aug 2002
Alexandria
2467_{10} Posts 
Yoyo is just about to finish a p65 test, see http://www.rechenkraft.net/yoyo/y_status_ecm.php

20120416, 15:23  #4 
(loop (#_fork))
Feb 2006
Cambridge, England
3^{3}·239 Posts 
I make that about a CPUdecade of ECM, so enough to want to proceed to polynomial selection. But msieve isn't quite plugandplay for polynomial selection at this level yet (see the fuss that I'm going to in the http://www.mersenneforum.org/showthread.php?t=16369 and the fact that I haven't devoted more time to carrying on with the selection)
Maybe I'm just being pessimistic  I'm moving house and job in the upcoming season and probably shouldn't volunteer for a sixmonth committment. Though it's probably more valuable than extending yet more aliquot sequences, and it has lessinteresting intermediate results so I might end up wasting less time watching numbers factor in the mornings than I do at the moment. Last fiddled with by fivemack on 20120416 at 15:26 
20120416, 17:57  #5  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
Interestingly enough, in this paper on the RH, the 7th endnote is a page and a half about B200 (though about half of that is an explanation of the Fermat 2PRP test).
Quote:
Fittingly enough, the 8th footnote is a twoliner stating that factorization has never been proven to be hard, and the 9th endnote is a one line link to GIMPS. FWIW (not much) I'd be willing to donate one core of an i72600K indefinitely. Last fiddled with by jasonp on 20120416 at 20:02 Reason: fixed markup 

20120416, 18:17  #6 
Sep 2009
1722_{8} Posts 
SNFS 204 is a piece of cake for RSALS (with a sextic or a quintic, a bit less so for a quartic)... but IIUC akruppa's and fivemack's posts, we're talking about a GNFS 204 here, and that is way out of reach for the poor little 14e, indeed
With a good poly, GNFS 175 could probably be done with 14e, as RSALS has already sieved a GNFS 169 task with 30bit LPs. But in the Aliquot 4788 team sievings, IIRC, 15e was used instead of 14e above 162163 digits. 
20120416, 19:21  #7  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
13^{2}·67 Posts 
Quote:
If anyone else would like to join in, please contact me. Paul 

20120416, 20:00  #8 
Tribal Bullet
Oct 2004
5×709 Posts 
Did the first job have (relations minus unique ideals) larger when the filtering started? I suspect the first job just had more oversieving; 7% extra relations actually is enough to make a big difference in matrix size.

20120416, 20:00  #9 
"Nancy"
Aug 2002
Alexandria
2467_{10} Posts 
I don't know how to make useful SNFS polynomials for Bernoulli numbers. Since there are composites with less than 200 digits left on Wagstaff's list, it appears that no one else does, either.

20120416, 21:13  #10 
Nov 2003
2^{2}×5×373 Posts 
There are recursion formulae for the Bernouilli's, but I seriously doubt that there is an algebraic closed form amenable to SNFS. Ask Sam.

20120417, 05:13  #11 
Romulan Interpreter
"name field"
Jun 2011
Thailand
3^{5}·41 Posts 
Stupid question: What (minimal/recommended) hardware does one need for such a huge job? (cores, gigs of memory). Maybe some people will want to, but they are not sure if the hardware they have is enough. Can one do it with his hardware at home, or he need all the university's lab for it? Estimation for completion?

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