Mertens' theorems

For Mertens's theorem on convergence of Cauchy products of series, see Cauchy product § Convergence and Mertens' theorem.
This article uses technical mathematical notation for logarithms. All instances of log(x) without a subscript base should be interpreted as a natural logarithm, also commonly written as ln(x) or loge(x).

In analytic number theory, Mertens' theorems are three 1874 results related to the density of prime numbers proved by Franz Mertens.[1]

In the following, let mean all primes not exceeding n.

  1. ^ F. Mertens. J. reine angew. Math. 78 (1874), 46–62 Ein Beitrag zur analytischen Zahlentheorie