All primes > 3 are of the form (6n + 1) or (6n - 1) where n is a natural number. Therefore the square of a prime will be of the form (36n^2 + 12n + 1) or (36n^2

All primes > 3 are of the form (6n + 1) or (6n - 1) where n is a natural number. Therefore the square of a prime will be of the form (36n^2 + 12n + 1) or (36n^2 - 12n + 1). The "interesting" properties pretty much follow from that.