Mertens' theorems
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For Mertens's theorem on convergence of Cauchy products of series, see Cauchy product § Convergence and Mertens' theorem.
In analytic number theory, Mertens' theorems are three 1874 results related to the density of prime numbers proved by Franz Mertens.[1]
This article uses technical mathematical notation for logarithms. All instances of log(x) without a subscript base should be interpreted as a natural logarithm, commonly notated as ln(x) or loge(x).
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In the following, let mean all primes not exceeding n.