International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 70, Pages 3889-3892

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

Copyright © 2004 L. J. P. Kilford. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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