Dirichlet's Theorem

Dirichlet's Theorem states that there are infinitely many prime numbers in any arithmetic sequence. Specifically, if you start with two numbers: a positive integer \( a \) (the starting point) and a positive integer \( d \) (the common difference), where \( a \) and \( d \) are coprime (they share no common factors other than 1), then the sequence \( a, a+d, a+2d, a+3d, \ldots \) will contain infinitely many prime numbers. This theorem highlights the richness of prime numbers within structured patterns.