344^49-1

  Henrik Olsen announces the complete factorization of the number
N=(344^49-1)/(344^7-1) from The Expanded Cunningham Table by the
Special Number Field Sieve (SNFS).  It was previously known that

        N = 7 * c106

where c106 is a 106 digit composite number given by

 c106 = 4901810841090858663562166539988061638554\
	1240592392390196534624133719083300605338\
	52995692964401604906937783

The two polynomials used were

        X^6 + X^5 + X^4 + X^3 + X^2 + X + 1 and
        X - 344^7

with common root 344^7 (mod N).

  The region sieved was b < 140000 and |a| < 262144.
A factorbase size of 100000 and large prime bound of
20M was used for both polynomials.
  A total of 1957609 relations was collected forming
a 206974 x 209407 matrix.

  The linear algebra stage took 2.6 CPU hours on a
350MHz P-II using about ~44M of memory, the square
root stage took 19.9 minutes and found the factorisation
in the first dependency checked.

  On Apr. 28, 2000 it was found that c106 = p43 * p63

  p43 = 7828645132567193929852782911953567269505621

  p63 = 626137825649971879400074251919682152428147285204450469423938523

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