Large primes over a large product

$\large \lim_{n\rightarrow\infty}\dfrac{p_{n^2}}{(P_n)^2}$

If $p_n$ is the $n\text{th}$ prime number and $P_n$ is the product of the first $n$ prime numbers, then find the value of the limit above.

This problem is a follow-up to this one .