Large primes over a large product

Calculus Level 4

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

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.
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