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 a non-negative integer. In other words, there are infinitely many primes which are
congruent to
a modulo d. The numbers of the form
a +
nd form an
arithmetic progression