409^49-1

  Henrik Olsen announces the complete factorization of the number
N=(409^49-1)/(409^7-1) from The Expanded Cunningham Table by the
Special Number Field Sieve (SNFS).  It was previously known that

        N = c110

where c is a  digit composite number given by

 c110 = 4924690438130704260864354018894708093894\
	1996610122422759760454492771808828285669\
	811578074992338344974985363791


The two polynomials used were

        X^6 + X^5 + X^4 + X^3 + X^2 + X + 1 and
        X - 409^7

with common root 409^7 (mod N).

  The region sieved was b < 123000 and |a| < 262144.
A factorbase size of 100000 and large prime bound of
20M was used for both polynomials.
  A total of 1830509 relations was collected forming
a 212454 x 213104 matrix.

  The linear algebra stage took 3.8 CPU hours on a
375MHz Celeron using about 40 MB of memory, the square
root stage took 12.7 minutes and found the factorisation
in the first dependency checked.

  On May 21, 2000 it was found that c110 = p41 * p69

  p41 = 86877611379588788843800601401840389127721

  p69 = 566853802714898481550011042506526852814853078532727381470869797503671

My NFSNET page
NFSNET homepage
Andy Steward's list
Cunningham Project homepage