A test for the primality of Fermat numbers 
,
with 
and 
. Then the two following conditions are equivalent:
1. 
is prime
and 
, where 
is the Jacobi symbol,
2. 
.
is usually taken as 3 as a first test.
Pépin's Test
See also
Fermat Number, Pépin's TheoremExplore with Wolfram|Alpha
References
Pépin, P. "Sur la formule
." Comptes Rendus 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 Web Resource. https://mathworld.wolfram.com/PepinsTest.html