Meissel–Mertens constant

The chisel - Mertens constant ( after Ernst Chisel ( 1826-1895 ) and Franz Mertens ) is a mathematical constant. Similar to the sum of the reciprocals of natural numbers ( harmonic series ), the sum of the reciprocal prime increases without bound (here, describes the set of prime numbers ). That both sums are of increasing number of links n arbitrarily large. The exact asymptotic growth is described by the two limits:

Here, the Euler's constant and M is the chisel - Mertens constant. The sum of reciprocal primes between 2 and n therefore grows asymptotically as the nested logarithm. It occurs mainly in number theory and function theory. There are numerous connections with other mathematical constants and rows. For example:

Here is the Möbius function and the Riemann zeta function. The numerical value of the chisel - Mertens constant