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

$K$ and $M$ are our inputs represented as integers.

Function Variant: Output the 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 $FNP$?

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

$K$ and $M$ are our inputs represented as integers.

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

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

Proof that calculating 2^n requires an exponential amount of digits as the result

Question

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

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

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

$K$ and $M$ are our inputs represented as integers.

Function Variant: Output the 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 $FNP$?