Notation on $ n > \pi(n) $, as $n$ grows, the difference grows

Question

Let $\pi$ be the prime counting function, and $n$ a positive integer greater than 3.

I would like to express in a math paper that that $ n > \pi(n) $ and as $n$ grows, the difference is getting bigger.

What is the correct notation for that?

Answer 1

What about $$\lim_{n\rightarrow \infty} (n-\pi(n))=\infty$$ ?