JP Journal of Algebra, Number Theory and Applications
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Abstract: Elite primes are prime
numbers, modulo which all but finitely many Fermat numbers,are quadratic nonresidues. This
definition has been extended using the generalized Fermat numbersand the associated primes are called
b-elite primes. We consider, as an
alternate generalization, the b-elite primes with respect to the sequence where b
is odd. We present some arguments for this modification and make necessary
adjustments to the classification results when the period length is one or two.
Furthermore, we search for elite and anti-elite primes to the base up to 2.68 billion.
Keywords and phrases: elite primes, generalized Fermat numbers.
