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 TheoremExplore with Wolfram|Alpha
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References
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 ResidueCite this as:
Weisstein, Eric W. "Selfridge-Hurwitz Residue." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Selfridge-HurwitzResidue.html