Show that if $\displaystyle p_n$ is the $\displaystyle n$-th prime, then $\displaystyle p_n \sim n \log(n)$ as $\displaystyle n \rightarrow \infty$.

In this section we have covered the Prime Number Theorem and Laplace transforms. However, I am still not sure how to prove this. I need some help on this problem. Thank you.