Dirichlet's theorem on primes in arithmetic progressions

From Number
Jump to: navigation, search

Template:Infinitude fact

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

Stronger facts

Easy cases

Related facts about infinitude

Conjectures/facts about the first Dirichlet prime

Conjectures/facts about Bertrand's postulate on Dirichlet primes

Conjectures/facts about contiguous blocks of Dirichlet primes

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.