Show that UPrime = {1^n : n ∈ N is prime} is in P I have this question to solve. According to my understanding, it basically requires a turing machine that outputs lines on the tape, with the number of the lines being any prime number. 

My idea is to take the AKS test's conclusion and making a case that since, calculating primes is a problem that can be solved in polynomial time complexity as already proven by AKS, hence this problem is also in P. 

Is this the right way? what would be a more formal/mathematical way of expressing this if it is?
Hint: Notice that your input is unary.