Photoelectric Primes

Algebra Level 5

Shivamani thinks that he has found a cubic polynomial $f(x)$ such that $f\left( n \right) =n$ -th prime number. He found that

$\begin{cases} {f(1) = 2} \\ {f(2) = 3 } \\ {f(3) = 5} \\ { f(4) = 7} \end{cases}$