# Photoelectric Primes 2:The rise of fallen

Algebra Level 4

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

$\begin{cases} {f(1) = 2} \\ {f(2) = 3 } \\ {f(3) = 5} \\ { f(4) = 7} \\ f(5) = 11\end{cases}$

Help him find the value of $f(6)$.

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