See this article: https://mathworld.wolfram.com/RiemannPrimeCountingFunction.html
Riemann's $R$ function is mentioned and $R$ is asymptotically equivalent to the prime counting function $\pi$ for $x\to\infty$. However I don't understand it when looking at this graph:
Asymptotic equivalence means that in this case the graph should get closer and closer to zero. However we can see that sometimes we get bigger spikes more far away from 0 when increasing $x$ values. Is there a number $X$ so that $\vert R(x)-\pi(x)\vert $ is monotonically decreasing to zero for all $x>X$? If yes, do we know where it is?