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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

 sum_(p<=x)1/p=lnlnx+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.


See also

Harmonic Series, Mertens Constant, Mertens Theorem, Prime Sums

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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 Theorem

Cite this as:

Weisstein, Eric W. "Mertens Second Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MertensSecondTheorem.html

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