@ARTICLE {, title = {Elitné prvočísla}, author = {Šolcová, Alena and Křížek, Michal}, journal = {Obzory matematiky, fyziky a informatiky}, year = {2006}, volume = {35}, number = {4}, pages = {1--6}, issn = {1335-4981}, abstract = {A prime number p is called elite, if only finitely many Fermat numbers Fm = 2^2^m 1 are quadratic residues modulo p. In this paper we give a survey on these primes. In particular, we show how to prove that 3, 5, 7, and 41 are elite primes. Then we introduce a necessary and sufficient condition for a prime to be elite. This condition was recently used to determine all elite primes up to 25 ·10^10 on computers. They can be applied as bases in the famous Pepin’s test. Several open problems concerning elite primes are presented as well.}, }