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.