TITLE: lower bound for the prime number function
QUESTION [8 upvotes]: Does there exist a function $f$ that is a lower bound of the prime number function $\pi$ with $f \sim \pi$?

REPLY [3 votes]: I found a more 'elegant' lower bound:
$$ \frac{n}{\log\,n} - 2 \leq \pi(n), \; n \geq 2 $$ Primality Testing in Polynomial Time