Honorable mention to Emmanuel of the 4th grade for determining that three is the only prime with this property. Numbers that are one less than a perfect square are always the product of one less than the square root of the perfect square times one more than the square root of the perfect square. The only way that this product could be prime is if one of the factors is one, and it is in this unique case that three is the product. (Given two squared, one less than this is one times three.)