letLet $n$$p_n$ be some integerthe $n$-th prime, then from Wikipedia iI got that :
$p_n \approx n(\ln n + \ln \ln n -1 + \frac{\ln \ln n-2}{\ln n}+\frac{6\ln \ln n-(\ln \ln n)^2-11}{\ln^2 n} $$p_n \approx n \left(\ln n + \ln \ln n -1 + \frac{\ln \ln n-2}{\ln n}+\frac{6\ln \ln n-( \ln \ln n)^2-11}{\ln^2 n} \right)$.
whatWhat is a better approximation that include $O(\frac{(\ln \ln n)^3}{\ln^3 n})$includes $O\big(\frac{(\ln \ln n)^3}{\ln^3 n}\big)$?
