The second theorem of Mertens 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.
Mertens Second Theorem
See also
Harmonic Series, Mertens Constant, Mertens Theorem, Prime SumsExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Mertens Second TheoremCite this as:
Weisstein, Eric W. "Mertens Second Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MertensSecondTheorem.html