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Problem 800

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Hybrid Integers

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

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混合整数

若一个整数可以表示为$p^q{q}^p$的形式，且$p\ne q$均为质数，则称其为混合整数。
例如，$800=2^5{5}^2$是一个混合整数。

定义$C(n)$为小于等于$n$的所有混合整数的数目。

已知$C(800)=2$，$C({800}^{800})=10790$。

求$C({800800}^{800800})$。

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