79

This number is a prime.

Let p be a prime number congruent to 3 (mod 4). When p is less than 79: (a) x^2 - py^2 = 5 has integer solutions iff p is square modulo 5; (b) px^2 - y^2 = 7 has integer solutions iff p is square modulo 7. Curiously, 79 is the smallest p (and the only p less than 223) that does not follow the same rules. [Yosei]