KnowraLinnik's theoremLinked fromLinked fromThe 7 pages that link to Linnik's theorem, each with the reason it gives.All 7Related 5Compared with 2Dirichlet's theorem on arithmetic progressionsRelated: It strengthens existence by giving a uniform bound for the first prime in each eligible class.Prime number theorem for arithmetic progressionsRelated: Quantitative distribution estimates help establish explicit bounds for finding primes in classes.Bombieri–Vinogradov theoremRelated: It addresses individual progressions through least-prime bounds, not aggregate error control.Chebotarev density theoremCompared with: It asks for an effective small-prime bound, while Chebotarev primarily gives asymptotic density.Siegel–Walfisz theoremRelated: Its proof uses progression estimates, including Siegel–Walfisz bounds for small moduli.Brun–Titchmarsh theoremRelated: It uses related sieve ideas to answer a different question about primes in progressions.Schinzel's theoremCompared with: Linnik studies primes in prescribed progressions, not primes at which a polynomial has a root.