Three new factors of Fermat numbers

175. R. P. Brent, R. E. Crandall, K. Dilcher and C. Van Halewyn, Three new factors of Fermat numbers, Mathematics of Computation 69 (2000), 1297-1304. MR 2000j:11194.

A preliminary version (with two factors and three authors) appeared as Technical Report TR-CS-97-11, Computer Sciences Laboratory, ANU, May 1997, 7 pp.

Abstract: dvi (3K), pdf (75K), ps (29K).

Paper: dvi (19K), pdf (166K), ps (63K).

Technical Report: dvi (17K), pdf (159K), ps (59K).


We report the discovery of a new factor for each of the Fermat numbers F13, F15, F16. These new factors have 27, 33 and 27 decimal digits respectively. Each factor was found by the elliptic curve method. After division by the new factors and previously known factors, the remaining cofactors are seen to be composite numbers with 2391, 9808 and 19694 decimal digits respectively.


For other factors of Fermat numbers, see [161].

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