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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 Theorem

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References

Pépin, P. "Sur la formule 2^(2^n)+1." 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 Test

Cite this as:

Weisstein, Eric W. "Pépin's Test." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PepinsTest.html

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