Sign of Difference between Prime-Counting Function and Eulerian Logarithmic Integral Changes Infinitely Often/Historical Note

Historical Note on Sign of Difference between Prime-Counting Function and Eulerian Logarithmic Integral Changes Infinitely Often
For values of $n$ lower than some large number, $\map \pi n - \displaystyle \int_2^n \frac {\d x} {\ln x}$ is greater than $0$.

However, in $1914$, proved that at some point $\map \pi n - \displaystyle \int_2^n \frac {\d x} {\ln x}$ switches to being less than $0$.

Furthermore, he proved that the lead changes an infinite number of times, if $n$ becomes large enough.