Selfridge-Hurwitz Residue
Let the Residue from Pépin's Theorem be
where
is a Fermat Number. Selfridge and Hurwitz use
A nonvanishing
indicates that is Composite for 
.See also Fermat Number, Pépin's Theorem
References
Crandall, R.; Doenias, J.; Norrie, C.; and Young, J. ``The Twenty-Second Fermat Number is Composite.'' Math. Comput. 64, 863-868, 1995.
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