Linnik's theorem in analytic number theory answers a natural question after Dirichlet's theorem on arithmetic progressions.
[1][2] Although Linnik's proof showed c and L to be effectively computable, he provided no numerical values for them.
It is known that L ≤ 2 for almost all integers d.[3] On the generalized Riemann hypothesis it can be shown that where
is the totient function,[4] and the stronger bound has been also proved.
Moreover, in Heath-Brown's result the constant c is effectively computable.