The Dirichlet prime number theorem states that if two integers a and b are relatively prime, then there are infinitely many primes of the form an+b. It is a natural question after the Dirichlet theorem to find an upper bound for the smallest prime having the form an+b. Linnik answered the question, which is called 'Linnik problem' now. This problem can be stated in terms of a certain character, and so the Linnik problem is extended to a question on automorphic representations. In this talk, I will talk about application of Langalnds program to the Linnik problem for automorphic representations.