Type: Article

On Cullen numbers which are both Riesel and Sierpinski numbers

Berrizbeitia, Pedro; Fernandes, J. G.; Gonzalez, Marcos J.; Luca, F.; Huguet, VJM;

Abstract:

We describe an algorithm to determine whether or not a given system of congruences is satisfied by Cullen numbers. We use this algorithm to prove that there are infinitely many Cullen numbers which are both Riesel and Sierpinski. (Such numbers should be discarded if you are searching prime numbers with Proth's theorem.) (C) 2012 Elsevier Inc. All rights reserved.