A powerful lead toward creating a proof can be found using the Croft Spiral Sieve:
Note, referencing the Croft Spiral Sieve, that all squared primes are either mod30,1 or mod30,19. Of these two, only where p = mod30,19 are both of which have primes positioned in p-2 (at mod30,17)mod30,29 and mod30,17, respectively). To see why this is the case, first explore this: http://www.primesdemystified.com, in order to understand this: http://primesdemystified.com/ChordSequenceFactorizations.html

