Pépin's Test
A test for the primality of Fermat numbers F_n=2^(2^n)+1, with n>=2 and k>=2. Then the two following conditions are equivalent:
1. F_n is prime and (k/F_n)=-1, where (n/k) is the Jacobi symbol,
2. k^((F_n-1)/2)=-1 (mod F_n).
k is usually taken as 3 as a first test.
See also
Fermat Number, Pépin's TheoremExplore with Wolfram|Alpha
WolframAlpha
References
Pépin, P. "Sur la formule 2^(2^n)+1." C. R. Acad. Sci. Paris 85, 329-333, 1877.Ribenboim, P. The Little Book of Big Primes. New York: Springer-Verlag, p. 62, 1991.Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 119-120, 1993.Referenced on Wolfram|Alpha
Pépin's TestCite this as:
Weisstein, Eric W. "Pépin's Test." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PepinsTest.html