Letting $\pi$ be the prime counting function and $\mathrm{Li}$ the logarithmic integral, Littlewood proved in his 1914 article "Sur la distribution des nombres premiers" that the difference $\pi(x)-\mathrm{Li}(x)$ changes sign infinitely many times; however, according to https://mathworld.wolfram.com/SkewesNumber.htmlWolfram Math World: Skewes Number, Kotnik proved that the smallest number for which this happens is greater than $10^{14}$.