For which positive integers n is $\displaystyle n^4 + 4^n$ prime?

I know 1 works. I know it can't be an even n because that would end up even, and thus not prime.

I checked 3, 5, and 7 and they all don't work. I don't know how to prove this as working or not though for bigger odd numbers. I feel like 1 might be the only answer, but not sure how to prove that other numbers do/don't work.