$\pi(x)$ is the prime counting function. This function is very important in number theory.
$\Phi(x)=Ad \int_2^xc^{Ab}dx,$ where $A=1/\log(x),$ where $d,c,b$ are constants. Is there any combination of these constants that will give a best approximation or an asymptotic bound on $\pi(x)?$ I've tried many combinations. The most recent ones I used are: $c=5/4,$ and $d,b=1,$ but I'm curious what combination will approximate $\pi(x)$ best and how to find that combination. Thanks.