The more natural conjecture, that every even number arises as the difference of two primes, was asked on math.SE years ago. That question remains open, and I have a hard time imagining that restricting to squares makes the problem any more tractable.

The more natural conjecture, that every even number arises as the difference of two primes, was asked on math.SE years ago. That question remains open, and I have a hard time imagining that restricting to squares makes the problem any more tractable.

EDIT: The conjecture that every even number is the difference of two primes is apparently sometimes called Maillet's conjecture.