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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