Journal of Integer Sequences, Vol. 9 (2006), Article 06.3.8

All Elite Primes Up to 250 Billion

Alain Chaumont
Laboratoire de Modélisation et Simulations Moléculaires "MSM"
Université Louis Pasteur
4, rue B. Pascal
67000 Strasbourg
France

Tom Müller
Institut für Cusanus-Forschung
Universität Trier
Domfreihof 3
54290 Trier
Germany

Abstract: A prime number p is called elite if only finitely many Fermat numbers 2 ^{2 n} +1 are quadratic residues of p. Previously only the interval up to 10⁹ was systematically searched for elite primes and 16 such primes were found. We extended this research up to 2.5 . 10¹¹ and found five further elites, among which 1,151,139,841 is the smallest and 171,727,482,881 the largest.

(Concerned with sequence A102742 .)

Received January 18 2006; revised version received August 21 2006. Published in Journal of Integer Sequences August 21 2006.