About

E’ giunto il momento di ridare alla Rete un po’ di quello che ho preso

Da wikipedia:

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 ≥ 0, or in other words: there are infinitely many primes which are congruent to a modulo d. Moreover, the sum of the reciprocals of such primes diverges.

This theorem extends Euclid’s theorem that there are infinitely many primes (in this case of the form 3 + 4n, which are also the Gaussian primes, or of the form 1 + 2n, for every odd number, excluding 1). Note that the theorem does not say that there are infinitely many consecutive terms in the arithmetic progression

a, a+d, a+2d, a+3d, …,

which are prime.