Dirichlet's theorem on arithmetic progressions

Theorem on the number of primes in arithmetic sequences

In number theory, 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. In other words, there are infinitely many primes that are congruent to a modulo d. The numbers of the form a + nd form an arithmetic progression a , a + d , a + 2 d , a + 3 d , … , {\displaystyle a,\ a+d,\ a+2d,\ a+3d,\ \dots ,\ } and Dirichlet's theorem states that this sequence contains infinitely many prime numbers.

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