Pépin's Test

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.

References

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.