Consider the function $f(x) = 5x^4 - 12x^3 + 30x^2 - 12x + 5$. Let $f(x_1) = p$, where $x_1$ and $p$ are non-negative integers, and $p$ is prime. Find with proof the largest possible value of $p$.

Let's think step by step and output the final answer within \boxed{}.
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