  We look at upper bounds for the count of certain primes related to the Fermat
numbers $F_n=2^{2^n}+1$ called elite primes. We first note an oversight in a
result of Krizek, Luca and Somer and give the corrected, slightly weaker upper
bound. We then assume the Generalized Riemann Hypothesis for Dirichlet L
functions and obtain a stronger conditional upper bound.
