https://en.wikipedia.org/wiki/Riemann_hypothesis#Consequence... lists several theorems that have been proved conditionally on the Riemann hypothesis being true. The most notable is probably the Goldbach conjecture, though that requires the generalized Riemann hypothesis.
It's a weak form of the Goldbach conjecture not the actual Goldbach conjecture itself. The weak form also has a proof that does not depend on the Riemann hypothesis.
