Prime Number Theorem And Intercepting The $\frac{1}{x}$ Line

 It's $\pi(x)=log(x)$ and not $\cfrac{x}{log(x)}$ and $p_n=n$ and not $nlog(n)$,

Whether it is an intercept on the $\cfrac{1}{p_n}$ curve by the $\cfrac{x}{p_n+2}$ line for a factor, as such a non prime, or a non-intercept on the $\cfrac{1}{p_n}$ curve by the $\cfrac{x}{p_n+2}$ line for prime number, both ride along the $\cfrac{1}{p_n}$ curve.

So, the number of primes, $\pi(x)$ at $x$ is less than $\int^{x}_1{\cfrac{1}{x}}=log(x)$

this however, does not give any information on the prime itself, $p_n$

$p_n=n$

Happy Lunar New Year.. reset system to spring and start over.