👉 Mailman's theorem is a fundamental concept in number theory that deals with the distribution of prime numbers and their gaps. It states that for any given positive integer \( k \), there are infinitely many pairs of primes \( (p, q) \) such that \( q - p = k \). In simpler terms, if you look at the difference between two prime numbers and find that this difference is always \( k \), then there are infinitely many such pairs. This theorem was first proven by Jacques Hadamard and Charles Jean de la Vallée Poussin independently in the late 19th century, using complex analysis and properties of the Riemann zeta function. Mailman's work not only confirmed this result but also provided deeper insights into the distribution of primes and their gaps, making it a cornerstone in analytic number theory.
