67^108+1

  Henrik Olsen announces the complete factorization of the number
N=(67^108+1)/(67^36+1) from Richard Brent's Factor Tables by the
Special Number Field Sieve (SNFS).  It was previously known that

        N = 1297 * 8641 * 487781269031809 * c110

where c110 is a 110 digit composite number given by

 c110 = 5491066382416259244342326921527452258260/
	5287889388073117374068227707275054879487/
	761662484990385027686201382017

The two polynomials used were

        X^6 - X^3 + 1 and
        X - 67^12

with common root 67^12 (mod N).

  The region sieved was b < 1000000 and |a| < 1048576.
A factorbase size of 200000 and large prime bound of
20M was used for both polynomials.
  A total of 2161919 relations was collected forming
a 564490 x 564720 matrix.
 
  The linear algebra stage took 17 CPU hours on a
400MHz P-II, using about 115 MB of memory, the square
root stage took 25 minutes and found the factorisation
in the Second dependency checked.

  On Feb 29, 2000 it was found that c110 = p54 * p57

  p54 = 161278104573929166365840295552095998416579961268302489

  p57 = 340471907015696530503090906033554515709260506230405990953

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