ANU Computer Science Technical Reports
TR-CS-96-02
Richard P. Brent.
Factorization of the tenth and eleventh Fermat numbers.
February 1996.
[POSTSCRIPT (193377 bytes)] [PDF (380293 bytes)]
Abstract: We describe the complete factorization of
the tenth and eleventh Fermat numbers. The tenth Fermat number is a product
of four prime factors with 8, 10, 40 and 252 decimal digits. The eleventh
Fermat number is a product of five prime factors with 6, 6, 21, 22 and 564
decimal digits. We also note a new 27-decimal digit factor of the thirteenth
Fermat number. This number has four known prime factors and a 2391-decimal
digit composite factor. All the new factors reported here were found by the
elliptic curve method (ECM). The 40-digit factor of the tenth Fermat number
was found after about 140 Mflop-years of computation. We discuss aspects of
the practical implementation of ECM, including the use of special-purpose
hardware, and note several other large factors found recently by ECM.
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