Number theory and hyper operators

[JmsNxn]

I'm wondering if anyone knows of any research of tetration and pentation and that whole gang in number theoretic areas. In the sense that we would only deal with natural x,y,n in the equation x [n] y.

I'm interested more specifically in results to do with primes. It's interesting because the same prime factors from x are the only ones which occur for n > 2 and y > 0. I'm thinking however more characteristic patterns reoccur.

Any help would be greatly appreciated!