78^99-1

  Henrik Olsen announces the complete factorization of the number
N=(78^99-1)/(78^33-1) from Richard Brent's Factor Tables by the
Special Number Field Sieve (SNFS).  It was previously known that

        N = 1783 * 225200075257 * c111

where c111 is a 111 digit composite number given by

 c111 = 1881585263728374501058108972873356759111\
	3061328068573431458081653943986528236139\
	2609606256855414694038854083263

The two polynomials used were

        X^6 + X^3 + 1 and
        X - 78^11

with common root 78^11 (mod N).

  The region sieved was b < 260000 and |a| < 1572864.
A factorbase size of 100000 and large prime bound of
20M was used for both polynomials.

  A total of 1998952 relations was collected forming a
   298K x 305K matrix.

The linear algebra stage took 5 hours on a 350MHz P-II, using about 64MB
of memory, the square root stage took 26 minutes and found the factorisation
in the second dependency checked.

  On Jan 13, 2000 it was found that c111 = p46 * p65
  
  p46 = 3390601780704001313469870728529432067982022571
  
  p65 = 55494138958945955425303121285487359758564762686069571585892597053

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