# Dirichlet's theorem on primes in arithmetic progressions

## Statement

Let  be relatively prime natural numbers. Then, there exist infinitely many primes  such that:

.

For fixed , the primes that are congruent to  modulo  are termed Dirichlet primes.

## Related facts

### Conjectures that generalize to higher degree polynomials

• Bunyakovsky conjecture is a conjecture for polynomials of degree two or more whose analogue for linear polynomials would be Dirichlet's theorem.