C(2,601-) Factored
------------------
M601 has been completely factored by the Special Number
Field Sieve (SNFS). It was previously known that
M601 = 3607 * 64863527 * c170
The factor 3607 was found by Riesel in 1957 and the factor
64863527 was found by Brillhart and Johnson in 1960. The
c170 is a 170 digit composite number given by
c170 = 354715929158469716117612845223357182401467887957184539934\
827018425775054703022731713537808507752796939456788348401\
72667458519819530578294315203146051414787170811175493759
On April 15, 1999 it was found that c170 = prp60 * prp110, where
prp60 = 6433907608968262728069255630596126855090392650310674568\
49993
prp110 = 5513226964341686180894070234940226491991504154775763376\
9331818430511033108848146620408728664776308505356579463
The factorization of M601 was 'Most Wanted' by the Cunningham
project. It was also the smallest number of the form 2^n-1 whose
complete factorization was not known. That distinction now goes to
M617.
The sieving was done with idle time on wiglaf, a beowulf with
32 233MHz PII processors. 9.5 million relations were collected
requiring 850 Mb in uncompressed ASCII format. The resulting matrix
size was 1342267 x 1364566. The linear algebra and square-root phases
were done at Centrum voor Wiskunde en Informatica (CWI) by Peter
Montgomery. The factorization was found on the fourth dependency.
Acknowledgments are due to Bob Silverman for his NFS code and
help and to Peter Montgomery for his help. Also to CWI and the School
of Mathematical Sciences at the University of Southern Mississippi for
the use of their computers.
C(2,592+) Factored
------------------
CWI announces the factorization of C(2,592+):
As of April, 1999 2^592 + 1 is the largest number factored by SNFS
(Special Number Field Sieve) on a single machine. This machine is medusa,
an SGI Origin 2000 with 24 250 Mhz processors at CWI (Centrum voor
Wiskunde en Informatica) in Amsterdam.
Sieving took 115 processor-days using 8 processors March 3-20, 1999.
for an 18-day period. A full filesystem delayed us for a week.
Linear algebra on a 1709640 x 1724589 matrix took 9.5 days
on one medusa processor between March 29 and April 11, 1999.
The square root step took under an hour.
C(2,592+)
* Algebraic factor 2^16 + 1 = 65537 already known
* c174 = prp74 * prp100 SNFS CWI
31474859175390153735107856059776876864094488913562623409377402922304455233
7857910537107244650997379051129365156632153489653285061191534178529543993418
529855775986967586885057
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