Recently I have been studying primes of various forms (and those forms are number theoretic and special functions). Let $\pi_{f(x)}(n)$ denote the number of primes less than $n$ which are of the form $f(x)$ for some $x\in\Bbb{Z}$. I first studied the function $\pi_{\phi(x)}(n)$. Few primes of suc...