71^108+1

  Henrik Olsen announces the complete factorization of the number
N=(71^108+1)/(71^36+1) from Richard Brent's Factor Tables by the
Special Number Field Sieve (SNFS).  It was previously known that

        N = 92106515344636659348487248548689 * c102

where c102 is a 102 digit composite number given by

 c102 = 2119877453214577250401095077786401435114\
	4647638931586467533821086618373205690123\
	7923480382587565129489

The two polynomials used were

        X^6 - X^3 + 1 and
        X - 71^12

with common root 71^12 (mod N).

  The region sieved was b < 2743997 and |a| < 1048576.
A factorbase size of 200000 and large prime bound of
20M was used for both polynomials.
  A total of 2135625 relations was collected forming
a 703864 x 704384 matrix.
 
  The linear algebra stage took 23.6 CPU hours on a
400MHz P-II using about 129 MB of memory, the square
root stage took 68 minutes and found the factorisation
in the third dependency checked.

  On Mar 28, 2000 it was found that c102 = p36 * p66

  p36 = 465441201027843802233773809520184049

  p66 = 455455479345877918415981036084869566767198876830375640735467222561

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