An application of the large sieve
Saburô Uchiyama · Proceedings of the Japan Academy Series A Mathematical Sciences · 1972
1. Let k be a positive integer and an integer with (/, k)--1, 0 =<l k.We denote by p(k, l) the least prime number in the arithmeti- cal progression kn/l (n-0, 1, 2,...).In 1936 P. Turin [2] proved under the assumption o the extended Riemann hypotheses for Dirichlet's L-unctions that we have or any fixed number p(k, l) < (k) (log k) except possibly for o((k))values of l, (1, k)--l, as koo, where (k) is the Euler totient function.