M617 Factored
-------------
M617 has been completely factored by the Special Number
Field Sieve (SNFS). It was previously known that
M617 = 59233 *
68954123297 *
c171
The p5 was found by Riesel in 1957 and the p11 found by
Brent and Suyama in 1981. The c171 is a 171 digit composite
factor given by
c171 = 133162933696720252644109076239739315294641129598\
571214674268232878869403201703608966454713865163\
367575359986404237817149731676559992850220509804\
718874844608767326097407871
On June 26,1999 it was found that c171 = prp51 * prp120,
where
prp51 = 1577519781152253854956475324210064781272294056\
44601
prp120 = 8441284558692203904329647194935146184026400044\
2557390949549814809580375481579281829664306776\
0548829906291314807571121271
The factorization of M617 was 'Most' wanted by the
Cunningham project[1] and is the smallest number of the form
2^n-1 whose complete factorization was not known. That
distinction now goes to M619.
The sieving was done by a group of 19 volunteers starting
May 7, 1999 and finishing on June 16, 1999. A total of
15986534 relations was collected requiring about 1.2 Gbytes
of memory in uncompressed ASCII format. The resulting matrix
was 1563691 x 1566436. 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 Ricardo Aguilera
Brian Briggs Gary Clayton
David Crandell Conrad Curry
Kelly Hall Philip Heede
Jim Howell Skip Key
Alex Kruppa Samuli Larvala
Don Leclair Ernst Mayer
Thomas Noekleby Henrik Oluf Olsen
Marcio de Moraes Palmeira Guillermo Ballester Valor
Paulo Vargas
Special thanks to Bob Silverman, Peter Montgomery, Alex
Kruppa, Don Leclair and Ernst Mayer. 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.
M619 is currently sieving by SNFS. It is on the Cunningham
projects 'More' wanted list. If you would like to donate some
of your CPU time visit [2] and download the siever for DOS or
linux. Source code is available on request to compile on other
platforms. You will need at least 21 Mbytes of free physical
memory.
[1] http://www.cs.purdue.edu/homes/ssw/cun/index.html
[2] ftp://ftp.netdoor.com/users/acurry/nfs
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