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We study the number of primes with a given primitive root and in anarithmetic progression under the assumption of a suitable form of thegeneralized Riemann Hypothesis. Previous work of Lenstra, Moree and Stevenhagenhas given asymptotics without an explicit error term, we provide an expliciterror term by combining their work with the method of Hooley regarding Artin'sprimitive root conjecture. We give an application to a Diophantine probleminvolving primes with a given primitive root.

Uniformly counting primes with a given primitive root and in an arithmetic progression