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{wiki=Mertens'_theorems}

One form of Mertens' theorem is
$$
\prod_{p\leq x}\left(1-\frac1p\right)
\sim\frac{e^{-\gamma}}{\log x}.
$$
Taking a ratio gives $\prod_{w\leq p\leq z}(1-1/p)\ll\log w/\log z$ for $2\leq w\leq z$.


Mertens theorem

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 150 / 1 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 150 / 1 / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 150 / 3 / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 150 / 1 / c / Solution

Mertens theorem

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Mertens theorem

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