Let the residue from Pépin's theorem be R_n congruent 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.

Fermat number | Pépin's theorem