Mertens Theorem is a result in number theory that provides an asymptotic formula for the sum of the reciprocals of the prime numbers. Specifically, it states that the sum of the reciprocals of the first n primes is approximately \log(\log(n)) , where \log denotes the natural logarithm. This theorem highlights the distribution of prime numbers and their density among integers. The theorem is named after the mathematician Franz Mertens, who contributed significantly to analytic number theory. Mertens Theorem is important for understanding the behavior of prime numbers and has implications in various areas of mathematics, including analytic number theory and prime number theory.