P608 Factored
NFSNET announces the complete factorization of P608 by the
Special Number Field Sieve (SNFS). It was known that
P608 = 641 *
14593 *
671233 *
6700417 *
620066693671553 * c149
where c149 is a 149 digit composite number given by
c149 = 407212607938109927686391811109168199291928333967395\
477888254196439811535677975754380014495465216898407\
44351212863529579604939708442787844678618504833
On October 7, 1999 it was found that c149 = p62 * p86
where
p62 = 729570376075162252904190636179938565056499153076206\
90006389889
p87 = 558153978412300305901519135681489925326736859374781\
699750217802894299569232242854570497
The factorization of P608 was 'Most Wanted' by the
Cunningham project [1] which has the goal of factoring
numbers of the form b^n +- 1 for b < 13. P608 was also the
smallest number of the form 2^n+1 whose complete
factorization was not yet known. The next smallest number
of this form that has not yet been completely factored is
P613.
The sieving was done by a group of 32 volunteers. A total
of 8.8M relations was collected forming a 1.294M x 1.296M
matrix. 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
Greg Childers Gary Clayton
Conrad Curry Russell Dixon
Geoffrey Faivre-Malloy Patrick Fossano
Jeff Gilchrist Kelly Hall
Philip Heede Jim Howell
Don Leclair Joe Leherbauer
Yaroslav Levchenko Chip Lynch
Ernst Mayer Holger Menz
Igors Mileika Thomas Noekleby
Alexis Nunes Henrik Oluf Olsen
Kirk Pearson Craig Renwick
Anthony Rumpel Keith Schmidt
Brian Schroeder Anastassios Sideridis
simon Sturle Sunde
Joe Williams David Willmore
Special thanks to Bob Silverman, Peter Montgomery and Don
Leclair. Also to CWI and the School of Mathematical
Sciences at the University of Southern Mississippi for the
use of their computers.
NFSNET is currently sieving 10,184+, a 'Most Wanted' number,
and 2,637+. If you would like to participate visit [2] and
download the siever, your computer will need at least 10Mb
of memory free.
[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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