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Old 2004-09-30, 11:25   #1
xilman's Avatar
May 2003
Down not across

11,503 Posts
Lightbulb Factorization of 3,491+.c234: p86 * p148

NFSNET is pleased to announce that the large prime factors of 3^491+1


with 86 digits and


with 148 digits.

No factors of this number, other than the trivial factor "4", were
previously known. It is one of the largest SNFS factorizations yet

We used the polynomials x^6+3 and x-m, which share a root m=3^82
modulo 3^491+1. The factorbases included primes up to 50 million on
each side and up to two large primes less than 1 billion were allowed
in relations. We sieved 42.1 million lines of length 90 million and
collected 80 million relations. Sieving began on 28th March 2004,
finished on 22nd August and used 36.4 kWU of effort.

Filtering and merging of the relations was done by Richard
Wackerbarth. The matrix produced had 8063681 rows, 8064612 columns and
a weight of 455165498. This matrix was far too big to run on any
single-cpu system available to us. Memory usage alone was well in
excess of 2Gb and it would have taken most of a gigahertz-year
processing time. When the project was started we believed that the
cluster at Microsoft Research would perform the linear algebra but it
was no longer accessible by the time the matrix was ready.

Herman te Riele very generously offered to run the matrix for us. He
used 32 nodes on SARA's "teras" computer and the computation took
close to three days elapsed, which is about 3 cpu-months.

The square root program ran on Richard's 2GHz G5 Macintosh. It took
10.5 hours to find the factors given above on the fifth dependency.

Many thanks to all the NFSNET sievers and, especially, to Herman te
Riele for running the linear algebra and thereby getting us out of an
embarrassing predicament.

Paul Leyland, for the NFSNET admin team.

Last fiddled with by Jeff Gilchrist on 2004-09-30 at 11:33
xilman is online now  
Old 2006-03-21, 05:13   #2
Wacky's Avatar
Jun 2003
The Texas Hill Country

32×112 Posts

Again, this is an anouncement, and not a question.
Wacky is offline  

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