Does anyone recognize this?

While thinking about Goldbach's conjecture, I came across this, but I don't know if it's something either trivial or already proven or disproven.

Anyway, the idea is this: for any odd prime, p, it's possible to find three other primes, i, j, k, distinct from p and from each other, such that .

For example:

2*2*5 - 11 = 3*3

2*2*7 - 3 = 5*5

2*2*13 - 3 = 7*7

I've verified it by computer up to 10,000, but I don't know what to do beyond that. (The program's running to 100,000 at the moment.)

On a side note, I think it may still work if you say i, j and k have to be odd primes, but I haven't tried that.

Edit: My program finished, verifying it up to 100,000.

2*7103*99133 - 17909 = 99991*99991