On the first sign change in Mertens' theorem
Volume 171 / 2015
Acta Arithmetica 171 (2015), 183-195
MSC: 11N05, 11Y35, 11M26.
DOI: 10.4064/aa171-2-5
Abstract
The function $\sum_{p\leq x} 1/p - \log\log(x) - M$ 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 $\exp(495.702833165)$.
