Dirichlet's Theorem states that there are infinitely many prime numbers in any arithmetic progression of the form a, a+d, a+2d, ..., where a and d are coprime integers (i.e., their greatest common divisor is 1). For example, if you take a = 2 and d = 3, the sequence would be 2, 5, 8, 11, 14, and so on, which contains infinitely many primes. This theorem was proven by the mathematician Peter Gustav Lejeune Dirichlet in 1837. It is significant in number theory as it extends the understanding of prime distribution beyond simple sequences, showing that primes can be found in structured patterns, provided certain conditions are met.