56^108+1

  Henrik Olsen announces the complete factorization of the number
N=(56^108+1)/(56^36+1) from Richard Brent's Factor Tables by the
Special Number Field Sieve (SNFS).  It was previously known that

        N = c126

where c126 is a 126 digit composite number given by

 c126 = 7405219642631179626291011881069721264443\
	7075703299639592925151066245845677292053\
	2803755678830083639482696326442087875482\
	746881

The two polynomials used were

        X^6 - X^3 + 1 and
        X - 56^12

with common root 56^12 (mod N).

  The region sieved was b < 540000 and |a| < 524288.
A factorbase size of 100000 and large prime bound of
20M was used for both polynomials.

  A total of 1956478 relations was collected forming a
   317k x 318k matrix.

The linear algebra stage took 5.6 CPU hours on a 350MHz P-II, using about 60MB
of memory, the square root stage took 46 minutes and found the factorisation
in the third dependency checked.

  On Jan 30, 2000 it was found that c126 = p50 * p76

  p50 = 77269422265903079004924816398089280538908780827441

  p76 = 9583635318442007025690296902527875768243215249221577221909512333830743909841

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