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.