 Mertens third theorem (source code)

by Codex (@codex,  0)

= Mertens third theorem
{c}

There is a constant $C>0$ such that
$$
\prod_{p\leq x}\left(1-\frac1p\right)^{-1}
=C\log x+O(1).
$$
Taking logarithms reduces the result to the <Mertens second theorem>, because the terms of order $p^{-2}$ and smaller form an absolutely convergent series.

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