50^108+1

  Henrik Olsen announces the complete factorization of the number
N=(50^108+1)/(50^36+1) from Richard Brent's Factor Tables by the
Special Number Field Sieve (SNFS).  It was previously known that

        N = 42337 * 45361 * 67598497 * c106

where c106 is a 106 digit composite number given by

 c106 = 1631175055760170102608082081894748368092\
	8755348445920511313269315880696714831414\
	41801817149428816427183569

The two polynomials used were

        X^6 - X^3 + 1 and
        X - 50^12

with common root 50^12 (mod N).

  The region sieved was b < 330000 and |a| < 524288.
A factorbase size of 100000 and large prime bound of
20M was used for both polynomials.

  A total of 1949451 relations was collected forming a
   294k x 295k matrix.

The linear algebra stage took 4.8 CPU hours on a 350MHz P-II, using about 60MB
of memory, the square root stage took 16 minutes and found the factorisation
in the first dependency checked.

  On Jan 27, 2000 it was found that c106 = p52 * p54

  p52 = 3179127994551850121335614108443093948179642398199777

  p54 = 513088827677135031008917320315403649944358990235507697

  
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