The twenty-second Fermat number is composite

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

doi:10.1090/S0025-5718-1995-1277765-9

The twenty-second Fermat number is composite
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by R. Crandall, J. Doenias, C. Norrie and J. Young PDF

Math. Comp. 64 (1995), 863-868 Request permission

Abstract:

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

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