Mertens' Theorem

Mertens' Theorem is a result in number theory that describes the average distribution of prime numbers among the integers. It states that the sum of the reciprocals of the prime numbers up to a certain limit grows at a specific rate, roughly corresponding to the logarithm of that limit. In simpler terms, as you look at larger and larger numbers, the way primes appear is fairly predictable, and this theorem provides a mathematical framework to understand their density and distribution in a more structured way.