We define a Cayley Table T from the structure (J,+) based on a subset J of Z containing prime numbers and their arithmetic inverses, which we then use as a model of gaps between primes of the form palpha - 3. Using definitions of the relationships between primes and their gaps derived from T, we prove the existence of infinitely many pairs of primes, (pn, pn+m), such that (pn+m - pn) = (palpha - 3) where n, alpha >= 3 and m >= 1 and pn is the nth prime. Finally, we use this result to show the existence of infinitely many pairs of prime numbers with a gap of 2.
MSC Classification: 11N05 , 11B05