Wei, Wang, On the Least Prime in an Arithmetic Progression, Acta Mathematica Sinica, New Series Chinese Journal of Mathematics, 7(3), 1991, pp. 279-288
Let q,k be positive integers. (q.k)=1, and P(k.q) be the smallest prime number satisfying p = k (mod q). In this paper, we prove that for q sufficiently large, one has P (k.q) << q. .