On the first sign change in Mertens' Theorem

Jan B\"uthe

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On the first sign change in Mertens' Theorem

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arxiv 1503.01277 v2 pith:DRHHVPFP submitted 2015-03-04 math.NT

On the first sign change in Mertens' Theorem

Jan B\"uthe This is my paper

classification math.NT

keywords changesignfirstbeforecalculatedfracfunctioninfinitely

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The function $\sum_{p\leq x} \frac{1}{p} - \log\log(x) - M$ is known to change sign infinitely often, but so far all calculated values are positive. In this paper we prove that the first sign change occurs well before $\exp(495.702833165)$.

On the first sign change in Mertens' Theorem

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