Photoelectric Primes 2:The rise of fallen

Algebra Level 4

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

{f(1)=2f(2)=3f(3)=5f(4)=7f(5)=11 \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)f(6).

This problem is original.
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