A prime number is a number with only two factors, itself and one (17 for example). A Mersenne number is a number which when added to one is a power of two (31 = 2^{5} – 1 for example). The base of a Mersenne number is the number which when two is taken to the power of that number equates to the Mersenne number add one (5 is the base of the Mersenne number 31 for example). Find the smallest Mersenne number such that the base of that Mersenne number is a prime number, but the Mersenne number itself is not.

Remember, to solve this puzzle and appear on the leaderboard, email both your solution and your source code (in any language) to lewiscornwall13@gmail.com. Good luck!!