> From owner-nmbrthry@LISTSERV.NODAK.EDU Sun Aug 5 22:27:19 2012
> Date: Sun, 5 Aug 2012 21:24:27 -0500
> Sender: Number Theory List
> From: "Hart, William"
> Subject: Factorisation of B200
We are happy to announce the factorization of the numerator of the 200th
Bernoulli number:
N = 389 * 691 * 5370056528687 * c204
c204 = p90 * p115
p90 = 149474329044343594528784250333645983079497454292838248852612270757617561057674257880592603
p115 = 2309888494878522213154166450313710367329236616136192088115975953987911840431532723141985023484762629703896050377709
The factorization of the 204-digit composite was made possible with the help
of many people:
- William Stein and Barry Mazur challenged us to factor this number
- Sam Wagstaff maintains a table of factorizations of numerators of Bernoulli
numbers at http://homes.cerias.purdue.edu/~ssw/bernoulli/bnum. According
to this table, the 200th Bernoulli number is the 2nd smallest index with
unfactored numerator (the first being the 188th Bernoulli number)
- Cyril Bouvier tried to factor the c204 by ECM up to 60-digit level, using
the TALC cluster at Inria Nancy - Grand Est
- yoyo at home tried to factor the c204 by ECM up to 65-digit level, using the
help of many volunteers of the distributed computing platform
http://www.rechenkraft.net/yoyo/
- after ECM was unsuccessful, we decided to factor the c204 by GNFS
- many people at mersenneforum helped for the polynomial selection. The best
polynomial was found by Shi Bai, using his implementation of Kleinjung's
algorithm in CADO-NFS:
http://www.mersenneforum.org/showthread.php?p=298264#post298264
- the sieving was performed by many volunteers at NFS at home, thanks to Greg
Childers. See http://escatter11.fullerton.edu/nfs for more details of
NFS at home.
This factorization showed that such a distributed effort might be feasible
for a new record GNFS factorization, in particular for the polynomial
selection. This was the largest GNFS factorization performed by NFS at home
to date, the second largest being 2^1040+1 at 183.7 digits.
- two independent runs of the filtering and linear algebra were done: one by
Greg Childers with msieve (http://www.boo.net/~jasonp/qs.html) using a
48-core cluster made available by Bill Hart, one by Emmanuel Thomé and
Paul Zimmermann with CADO-NFS (http://cado-nfs.gforge.inria.fr/), using the
Grid 5000 platform.
- the first linear algebra run to complete was the one with CADO-NFS, thus we
decided to stop the other run.
Bill Hart