65^108+1

  Henrik Olsen announces the complete factorization of the number
N=(65^108+1)/(65^36+1) from Richard Brent's Factor Tables by the
Special Number Field Sieve (SNFS).  It was previously known that

        N = 41330953 * c123

where c123 is a 123 digit composite number given by

 c123 = 8193816977208708200562990410752223022017\
	2457162362800129157257241709496038916863\
	4126570609008683494594312719696985128834\
	617

The two polynomials used were

        X^6 - X^3 + 1 and
        X - 65^12

with common root 65^12 (mod N).

  The region sieved was b < 800000 and |a| < 1048576.
A factorbase size of 200000 and large prime bound of
20M was used for both polynomials.
  A total of 2023476 relations was collected forming
a 580069 X 581868 matrix.
 
  The linear algebra stage took 14 CPU hours on a
400MHz P-II, using about 100 MB of memory, the square
root stage took 20 minutes and found the factorisation
in the first dependency checked.

  On Feb 12, 2000 it was found that c123 = p53 * p70

  p53 = 82752024826980784879415044606474973792900051662547281

  p70 = 9901651342478286951039307972750736024898420585780092986965544256791657

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