The second theorem of Mertens states that the asymptotic form of the harmonic series for the sum of reciprocal primes is given by sum_(p<=x) 1/p = ln ln x + B_1 + o(1), where p is a prime, B_1 is a constant known as the Mertens constant, and o(1) is a Landau symbol.

harmonic series | Mertens constant | Mertens theorem | prime sums