66^108+1

  Henrik Olsen announces the complete factorization of the number
N=(66^108+1)/(66^36+1) from Richard Brent's Factor Tables by the
Special Number Field Sieve (SNFS).  It was previously known that

        N = 1900156645081 * 997291722339141913 * c101

where c101 is a 101 digit composite number given by

 c101 = 5364777811625784611351699905509100048588\
	1051112965146242999844174512755392677678\
	871653462611327526097

The two polynomials used were

        X^6 - X^3 + 1 and
        X - 66^12

with common root 66^12 (mod N).

  The region sieved was b < 988380 and |a| < 1048576.
A factorbase size of 200000 and large prime bound of
20M was used for both polynomials.
  A total of 2159754 relations was collected forming
a 539185 X 539288 matrix.
 
  The linear algebra stage took 15.75 CPU hours on a
400MHz P-II, using about 110 MB of memory, the square
root stage took 43 minutes and found the factorisation
in the Second dependency checked.

  On Feb 19, 2000 it was found that c101 = p44 * p58

  p44 = 15915530970669877644827794199017137485065417

  p58 = 3370781547604241500789771169216236601320733431261414532041

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