International Journal of Mathematics and Mathematical Sciences 
Volume 2004 (2004), Issue 70, Pages 3889-3892
doi:10.1155/S0161171204403226

A generalization of a necessary and sufficient condition for primality due to Vantieghem

L. J. P. Kilford

 The University of Oxford, Mathematical Institute, 24–29 Street Giles', Oxford OX1 3LB, UK
Received 10 March 2004

Abstract

We present a family of congruences which hold if and only if a natural number n is prime.