M619 Factored
NFSNET announces the complete factorization of M619 by the
Special Number Field Sieve (SNFS). It was known that
M619 = 110183 *
710820995447 *
c170
The p6 was found by Riesel in 1957 and the p12 was found by
Brent in 1982. The c170 is a 170 digit composite number given
by
c170 = 2777745649328972688810916397062812010257130991427\
9358229355570999339261261987727468953261023572569\
4412280877801216942614553583803018713669960278199\
16671992902540756030687
On August 10, 1999 it was found that c170 = prp66 * prp105
where
prp66 = 10937868167107529719569248023421390812364256019\
2251038455204252439
prp105 = 25395676807316421450129702311820691730986108266\
99935824506978163832424511153655290711704204524\
55686291833
The factorization of M619 was 'More' wanted by the
Cunningham project[1] and the smallest number of the form
2^n-1. That distinction now goes to M629.
A total of 16446966 relations was collected from 28
volunteer sievers between June 3, 1999 and July 30, 1999. 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
Rich Brown Gary Clayton
David Crandell Conrad Curry
Geoffrey Faivre-Malloy Patrick Fossano
Pocza Gabor Kelly Hall
Philip Heede Greg Hewgill
Jim Howell Alex Kruppa
Samuli Larvala Don Leclair
Yaroslav M. Levchenko Chip Lynch
Ernst Mayer Holger Menz
Thomas Noekleby Henrik Oluf Olsen
Craig Renwick Brian Schroeder
Simon Sturle Sunde
Tom Womack Serge Zakharov
Special thanks to Bob Silverman, Peter Montgomery, Don
Leclair and Henrik Oluf Olsen. Also to CWI, the Department of
Computer Sciences at the Technical University Munich and the
School of Mathematical Sciences at the University of Southern
Mississippi for the use of their computers.
2,608+ is currently being sieved and M629 is next. If you
want to donate your CPU cycles go to the NFSNET homepage[2] for
instructions on how you can help.
[1] http://www.cs.purdue.edu/homes/ssw/cun/index.html
[2] http://orca.st.usm.edu/~cwcurry/nfs/nfs.html
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