93^99+1

  Henrik Olsen announces the complete factorization of the number
N=(93^99+1)/(93^33+1) from Richard Brent's Factor Tables by the
Special Number Field Sieve (SNFS).  It was previously known that

        N = 109 * 271 * 397 * 55171 * c119

where c119 is a 119 digit composite number given by

 c119 = 1285219934720472092500982270861444552908\
	9716467776126259193649995113158019816855\
	821909101687809576564402737155927357049


The two polynomials used were

        X^6 - X^3 + 1 and
        X - 93^11

with common root 93^11 (mod N).

  The region sieved was b < 228000 and |a| < 1572864.
A factorbase size of 200000 and large prime bound of
50M was used for both polynomials.

  A total of 4513715 relations was collected forming a
   532 x 533k matrix.

The linear algebra stage took 17 CPU hours on a 350MHz P-II, using about 108MB
of memory, the square root stage took 28 minutes and found the factorisation
in the first dependency checked.

  On Jan 25, 2000 it was found that c119 = p58 * p62
  
  p58 = 1046593170659606668874902551966945873371864086207782336319
  
  p62 = 12280033643927495570668664069677437412854414411951577723673671

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