Mertens' Second Theorem

Mertens' second theorem states that the asymptotic form of the harmonic series for the sum of reciprocal primes is given by

where  is a prime,  is a constant known as the Mertens constant, and  is a Landau symbol.

REFERENCES:

Havil, J. Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, p. 109, 2003.

Tenenbaum, G. and Mendes-France, M. The Prime Numbers and Their Distribution. Providence, RI: Amer. Math. Soc., p. 22, 2000.