Dirichlet's Theorem on Primes in Arithmetic Progressions

Dirichlet's theorem states that for any two positive integers that are coprime (share no common factors other than 1), there are infinitely many prime numbers that form an arithmetic sequence with those two numbers as the first term and the difference. For example, if the first number is 3 and the difference is 4, the sequence 3, 7, 11, 15, 19, ... contains infinitely many primes (3, 7, 11, 19). The theorem confirms primes are evenly distributed among all such sequences where the initial two numbers are coprime, ensuring an infinite supply of primes in various linear patterns.