405^49-1

  Henrik Olsen announces the complete factorization of the number
N=(405^49-1)/(405^7-1) from The Expanded Cunningham Table by the
Special Number Field Sieve (SNFS).  It was previously known that

        N = 10781 * c106

where c106 is a 106 digit composite number given by

 c106 = 3023095932688927394238140916230773315262\
	2476805564484438058655272205271383588698\
	97213779414107548578811871

The two polynomials used were

        X^6 + X^5 + X^4 + X^3 + X^2 + X + 1 and
        X - 405^7

with common root 405^7 (mod N).

  The region sieved was b < 140300 and |a| < 262144.
A factorbase size of 100000 and large prime bound of
20M was used for both polynomials.
  A total of 1947194 relations was collected forming
a 212454 x 213104 matrix.
 
  The linear algebra stage took 2.7 CPU hours on a
375MHz Celeron using about ~45M of memory, the square
root stage took 11.6 minutes and found the factorisation
in the first dependency checked.

  On May 18, 2000 it was found that c106 = p52 * p55

    p52 = 1039994369909403327639066252669922057135109132779531

    p55 = 2906838748513876389487877001991018660120320041361158141

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