An integer of the form $p^q{q}^p$ with prime numbers $p\ne q$ is called a hybrid-integer.
For example, $800=2^5{5}^2$ is a hybrid-integer.

We define $C(n)$ to be the number of hybrid-integers less than or equal to $n$.
You are given $C(800)=2$ and $C({800}^{800})=10790$.

Find $C({800800}^{800800})$.