Answer: 37
Explanation: To find the greatest two-digit prime number that is one greater than a perfect square, we can start by listing perfect squares in the two-digit range and check if any of them are prime numbers.
The two-digit perfect squares are 4, 9, 16, 25, 36, 49, 64, and 81. Adding 1 to each of these numbers, we get 5, 10, 17, 26, 37, 50, 65, and 82.
Among these numbers, only 17 and 37 are prime numbers. Since we are looking for the greatest two-digit prime number, the answer is 37.