There are some interesting statements that are equivalent to the Riemann Hypothesis. What "equivalent" means is that if the statement is true then RH must be true, and if RH is true then the statement must be true.

Here's one I find particularly nice.

Let s(n) = the sum of the divisors of n, for a positive integer n. For example s(12) = 1 + 2 + 3 + 4 + 6 + 12 = 28.

Let H(n) = 1 + 1/2 + 1/3 + ... + 1/n.

The RH is equivalent to the claim that for every integer n >= 1:

s(n) <= H(n) + exp(H(n)) log(H(n))

This is due to Jeffry C. Lagarias. Here's his paper showing the equivalence: https://arxiv.org/abs/math/0008177