84^99-1

  Henrik Olsen announces the complete factorization of the number
N=(84^99-1)/(84^33-1) from Richard Brent's Factor Tables by the
Special Number Field Sieve (SNFS).  It was previously known that

        N = 379 * 926909299 * c116

where c116 is a 116 digit composite number given by

 c116 = 2862572079284290482228995790463810353122\
	4350988836384826443253787865952824065871\
	763777447361602066528815076485035201


The two polynomials used were

        X^6 + X^3 + 1 and
        X - 84^11

with common root 84^11 (mod N).

  The region sieved was b < 313000 and |a| < 1572864.
A factorbase size of 100000 and large prime bound of
20M was used for both polynomials.

  A total of 1944648 relations was collected forming a
   358k x 359k matrix.

The linear algebra stage took 6.9 hours on a 350MHz P-II, using about 64MB
of memory, the square root stage took 29 minutes and found the factorisation
in the second dependency checked.

  On Jan 13, 2000 it was found that c116 = p47 * p69
  
  p47 = 93427641669673979896042961119658551000444690249
  
  p69 = 306394556057114222214398415309146939281417374480965956808719844037049

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