  We study the number of primes with a given primitive root and in an
arithmetic progression under the assumption of a suitable form of the
generalized Riemann Hypothesis. Previous work of Lenstra, Moree and Stevenhagen
has given asymptotics without an explicit error term, we provide an explicit
error term by combining their work with the method of Hooley regarding Artin's
primitive root conjecture. We give an application to a Diophantine problem
involving primes with a given primitive root.
