The twenty-second Fermat number is composite

Author:

Crandall R.,Doenias J.,Norrie C.,Young J.

Abstract

We have shown by machine proof that F 22 = 2 2 22 + 1 {F_{22}} = {2^2}^{^{22}} + 1 is composite. In addition, we reenacted Young and Buell’s 1988 resolution of F 20 {F_{20}} as composite, finding agreement with their final Selfridge-Hurwitz residues. We also resolved the character of all extant cofactors of F n , n 22 {F_n}, n \leq 22 , finding no new primes, and ruling out prime powers.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

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