Question 550132
The expression factors to (n-3)(n^2 - 11n + 31). Since we want a prime number, either n-3 or n^2 - 11n + 31 must be equal to 1 (or -1). Solving for n, we obtain n = 2, 4, 5, or 6. Here are the values we obtain when we replace n into the given expression:


n = 2 --> -13
n = 4 --> 3
n = 5 --> 2
n = 6 --> 3


The values n = 4, 5, 6 produce prime numbers, so the answer is 3.