Selfridge-Hurwitz Residue

Let the residue from Pépin's theorem be

 R_n=3^((F_n-1)/2) (mod F_n),

where F_n is a Fermat number. Selfridge and Hurwitz use

 R_n (mod 2^(35)-1,2^(36),2^(36)-1).

A nonvanishing R_n (mod 2^(36)) indicates that F_n is composite for n>5.

See also

Fermat Number, Pépin's Theorem

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Crandall, R.; Doenias, J.; Norrie, C.; and Young, J. "The Twenty-Second Fermat Number is Composite." Math. Comput. 64, 863-868, 1995.

Referenced on Wolfram|Alpha

Selfridge-Hurwitz Residue

Cite this as:

Weisstein, Eric W. "Selfridge-Hurwitz Residue." From MathWorld--A Wolfram Web Resource.

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