On May 20th 2003, NFSNET completed the factorization of 12^197-1.

The factors of the C212 cofactor are:

p70 = 1159476869764471212326146050644254795037901851473126597328861230702273 and

p143 = 311207960075022672724824491401220042557441917386312989845200507374527102 \
           84343466737369062910174217774560583587229141001505348482068028243056797

We used SNFS with the polynomials x^6 - 12 and m-x which share a root m=12^33 mod 12^197-1. We used primes up to 50 million on the rational and algebraic sides, with up to two large primes < 500 million on each side.

The sieving stage was performed by NFSNET participants using 80 machines from 38 participants. Sieving began on March 26th, 2003 and finished on May 2nd, 2003.

Approximately 9.8M lines were sieved and 43 million relations were found. The filtering stage reduced these to a matrix which had 5,139,074 rows and 5,167,041 columns. Primes less than 120 were excluded providing a savings in matrix weight of 47,243,415 and a final matrix weight of 275,931,954. The matrix had an average of 53.63 set bits per row and 53.39 set bits per column.

The linear algebra was performed on the MSRC cluster using 30 of its 1Ghz P-III CPUs. It began on May 12th and finished after just over 177 hours (about 7.4 days). The cpus were running at approximately 50% capacity and so the total cpu time was around 2,650 hours. The discrepancy between the CPU time and the elapsed time is explained by the latency in the inter-CPU communications via gigabit ethernet.

During the square root phase the factors were found on the first dependency which completed after 3 hours on a 2.5GHz-P4 workstation.

For more information visit http://www.nfsnet.org.

The NFSNET administrators:

Chris Card
Jeff Gilchrist
Don Leclair
Paul Leyland
Richard Wackerbarth

Contributors to the 12^197-1 factorization:

Brian Beesley, Chris Card, Decio Luiz Gazzoni Filho, Jeff Gilchrist, Francois Grieu, Rich Harms, Alex Kruppa, Rick Lavoie, Don Leclair, Paul Leyland, Andreas Pipp, Jeramy Ross, Igor Schein, Martin Schroeder, Richard Wackerbarth and 23 others who have not selected to be listed here.