Find all natural numbers $n$ such that $n$, $n^2+10$, $n^2-2$, $n^3+6$, and $n^5+36$ are all prime numbers.
Source: Hong Kong 2016 TST 1
Tags: number theory
Find all natural numbers $n$ such that $n$, $n^2+10$, $n^2-2$, $n^3+6$, and $n^5+36$ are all prime numbers.