Journal of Integer Sequences, Vol. 10 (2007), Article 07.9.4

On Anti-Elite Prime Numbers

Tom Müller
Institut für Cusanus-Forschung
an der Universität und der Theologischen Fakultät Trier
Domfreihof 3
54290 Trier


An odd prime number p is called anti-elite if only finitely many Fermat numbers are quadratic non-residues to p. This concept is the exact opposite to that of elite prime numbers. We study some fundamental properties of anti-elites and show that there are infinitely many of them. A computational search among all the numbers up to 100 billion yielded 84 anti-elite primes.

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(Concerned with sequence A128852.)

Received June 28 2007; revised version received September 18 2007. Published in Journal of Integer Sequences, September 20 2007.

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