Around the Wilson's theorem

Jan Górowski, Adam Łomnicki


In this paper some known conditions and new congruences characterising prime numbers are given. Some of them are obtained by the generalised Wilson theorem given by Gauss. The elementary proof of this theorem is also presented.


prime number, Wilson’s theorem, congruence


Dence, J. B., Dence, T. P.: 1995, Anecessary and sufficient conditions for twin primes, Missouri J. Math. Sci. 7(3), 129-131.

Ribenboim, P.: 1991, The little book of big primes, Springer Verlag, New York.

Sierpiński, W.: 1988, Elementary theory of numbers. second edition, North-Holland PublishingCo, Amsterdam.

Yan, S. Y.: 2006, Number theory for computing, Springer Verlag, Berlin.

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