On the magnitude of the least prime primitive root (Q923617)

The results of this paper are estimates (assuming the Generalised Riemann Hypothesis) for the least prime primitive root G(p) modulo a prime p. Thus the principal theorem is that if the GRH is true then for any monotone increasing function f satisfying \[ \lim_{x\to \infty}f(x)=\infty,\quad \exists A : f(x)\ll (\log x)^ A,\quad f(x)\ll f(x/\log x) \] the estimate \(G(p)\ll f(p)\) holds for all primes \(p<x\) with at most \(O(\pi (x)/\log f(x))\) exceptions. The method is a substantial extension of Hooley's proof (assuming GRH) of Artin's conjecture.