The sum of the squares of three consecutive odd numbers is 2531. How many of these numbers are prime numbers?

Two of the three numbers are prime.

Let the middle number be n; the three are n-2, n, n+2.

Sum of squares = 3n^2 + 8 = 2531, so 3n^2 = 2523.

n^2 = 841, so n = 29; the numbers are 27, 29, 31.

27 = 3^3 is not prime, while 29 and 31 are prime.