 Mertens' theorems

ID: mertens-theorems

\prod_{p \leq x} (1 - \frac{1}{p}) \sim \frac{e ^{- γ}}{l o g x} .

Taking a ratio gives

\prod_{w \leq p \leq z} (1 - 1/ p) ≪ lo g w / lo g z

for

2 \leq w \leq z

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