# Wilson theorem

Let be a prime number. Then the number is divisible by . The theorem was first formulated by E. Waring (1770) and is, according to him, due to J. Wilson. It was proved by J.L. Lagrange in 1771. A primality test for integers follows from Wilson's theorem: A natural number will be prime if and only if

This test is not recommended for practical use, since the factorial involved rapidly becomes very large.

#### References

 [1] A.A. Bukhshtab, "Number theory" , Moscow (1966) (In Russian) [2] E. Trost, "Primzahlen" , Birkhäuser (1953) [3] I.M. [I.M. Vinogradov] Winogradow, "Elemente der Zahlentheorie" , R. Oldenbourg (1956) (Translated from Russian)

[4] Amrik Singh Nimbran, Some Remarks on Wilson's Theorem, 'The Mathematics Student',Indian Mathematical Society, Vol. 67, Nos. 1–4 (1998), 243–245