Photoelectric Primes

Algebra Level 4

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

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

Help him find the value of \(f(5)\).

This problem is original.
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