On Feb 4th 2003, NFSNET completed the factorization of 5^289+1.

The factors of the C156 cofactor are:

p62 = 12156847076444678217726556516258597180670422099432269314205601 and

p95 = 106930627032805685699324173924866262201786687728458305580891702559225934 09573680162209144318227

We used SNFS with the polynomials mx-1 and m^6+5 which share a root m=5^(-48) mod 5,289+. As in the previous factorization, we used primes up to 40 million on the rational side and 50 million on the algebraic, with up to two large primes < 500 million on each side.

The sievers found 42,819,180 relations, of which 37,605 were duplicates. The filtering stage reduced these to a matrix which had 4,377,803 rows and 4,388,598 columns. The linear algebra took 101 hours elapsed, circa 1500 hour total cpu time on 30 PIII-1000 processors of the MSRC cluster. The factors were found on the second dependency. Each dependency took 80 minutes to process on a 2.53GHz P4 machine.

Once more, thanks are due to CWI for the use of their (modified) software.

The NFSNET admins:

Jeff Gilchrist
Don Leclair
Paul Leyland
Richard Wackerbarth