# Exponential Prime Powers

Let $$N$$ be the sum of all prime powers that can be written as $$4^n+n^4$$ for some positive integer $$n$$.

What are the last 3 digits of $$N$$?

Details and assumptions

A prime power is a number of the form $$p^k$$, where $$p$$ is a prime and $$k$$ is a positive integer. Examples: 3,9,16.

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