# 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

## Question

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 $$FNP$$?