The question is:
input: encoding of a TM M
question: is there some input y, such that when M runs on y, the exact number of steps M goes through is prime.
the answer was RE\R and than it is deleted (with the note this is a midnight correction) and it says none of the above.
What is incorrect with following construction?
TM M': Start to scan in parallel all the possible
inputs, and run M on each of them. For each, keep count of the number
of states you've been in so far. Whenever M stops on one of the
inputs after being in p states, and p is prime, stop and accept.
Is it possible there is a mistake in the answers?