Linnik's theorem

Linnik's theorem in analytic number theory answers a natural question after Dirichlet's theorem on arithmetic progressions. It asserts that there exist positive c and L such that, if we denote p(a,d) the least prime in the arithmetic progression where n runs through the positive integers and a and d are any given positive coprime integers with 1 ≤ a ≤ d − 1, then: The theorem is named after Yuri Vladimirovich Linnik, who proved it in 1944. Although Linnik's proof showed c and L to be effectively computable, he provided no numerical values for them.