Mertens Second Theorem

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


where p is a prime, B_1 is a constant known as the Mertens constant, and o(1) is a Landau symbol.

See also

Harmonic Series, Mertens Constant, Mertens Theorem, Prime Sums

Explore with Wolfram|Alpha


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 Theorem

Cite this as:

Weisstein, Eric W. "Mertens Second Theorem." From MathWorld--A Wolfram Web Resource.

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