Two statements I find quite interesting involve Farey sequences, and, very roughly, they can be interpreted as saying that elements of Farey sequence are "not far" from being evenly distributed in the unit interval.

To be precise, suppose $n$-th Farey sequence is $0=a_{0,n}<a_{1,n}<\dots<a_{m_n,n}=1$ and let $d_{k,n}=a_{k,n}-\frac{k}{m_n}$. Then RH is equivalent to any of the two statements below:

• $\sum_{k=0}^{m_n} d_{k,n}^2=O(n^{-1+\varepsilon})$ for any $\varepsilon>0$ as $n\rightarrow\infty$.
• $\sum_{k=0}^{m_n} |d_{k,n}|=O(n^{1/2+\varepsilon})$ for any $\varepsilon>0$ as $n\rightarrow\infty$.