Assume that I have written a program that will generate and emit as output all the prime numbers

in order $($this is easy to do$).$ Assuming no additional information about the primes other than the

fact that this program can generate them, the set of prime numbers $(P)$ is seen to be $($choose and

explain your choice$)$:

Turing$-$decidable $...$ or $...$

Turing$-$recognizable.