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Mathematics of Computation

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The twenty-second Fermat number is composite

Authors: R. Crandall, J. Doenias, C. Norrie and J. Young
Journal: Math. Comp. 64 (1995), 863-868
MSC: Primary 11Y11; Secondary 11A51
MathSciNet review: 1277765
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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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Article copyright: © Copyright 1995 American Mathematical Society

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