An alleged primary motivator for the RH is so that we can bound the error term $|\text{Li}(x) - \pi(x)|$ by a factor of $O(\sqrt{x}\log x)$. However, I also learned about Riemann's explicit formula $R(x)$ that converges, upon addition of the harmonics $C_i(x, \theta_i)$, where $\theta_i$ is the R...
