For any two coprime positive integers a and d, there are infinitely many primes of the form a plus n times d. Proved using analytic techniques involving what are now called Dirichlet L-functions, it was an early triumph of analytic number theory.
Facts
StatementDirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n is also a positive integer. 1 Classification
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Sources
1. Dirichlet's Theorem on Arithmetic Progressions (Wikipedia)
Wikimedia Foundationlead section, first paragraph
Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n is also a positive integer.
lead section, naming sentence
The theorem is named after the German mathematician Peter Gustav Lejeune Dirichlet, who proved it in 1837.
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