The problem is interesting, but being vague, numerous solutions seem possible:
a1: 2 is the smallest prime
a2: 2 is the only even prime.
a3: 2 is the only even number equal to its factorial.
b1: this is the only triplet of a square, a prime and a triangular number in a consecutive sequence
b2: this is the only triplet of digits in sequence in which the middle number's factorial is equal to the product of all the members
b3: this is the only triplet of a square, a prime and a perfect number in a consecutive sequence.
Need I CONTINUE?
Let's wait and compare with the official solution
??? How is it possible to edit a typo in my comment's title?
Edited on September 2, 2014, 8:18 pm