Editing Mertens' theorems (section)

=== Relation to sieve theory<span class="anchor" id="Mertens' third theorem and sieve theory"></span> ===

An estimate of the probability of <math>X</math> (<math>X \gg n</math>) having no factor <math>\le n</math> is given by

:<math>\prod_{p\le n}\left(1-\frac1p\right)</math>

This is closely related to Mertens' third theorem which gives an asymptotic approximation of

:<math>P(p \nmid X\ \forall p \le n) = \frac{1}{e^\gamma \log n }</math>