Is it incorrect too say that this function problem cannot be in $FNP$?

Decision Problem: Is $ 2^k$ + $ M$ NOT a prime?

Function Variant: Output the non-prime result of $ 2^k$ + $ m$

We can consider, $ M$ = $ 0$ .

Proof that calculating 2^n requires 2^n digits as the result


Is it true that a non-deterministic machine cannot output $ 2^n$ digits in polynomial time?

Does this mean that the problem is not in $ FNP$ ?