We have an approximate expression of how many prime numbers there are less than N, as N gets larger. If the Riemann hypothesis is true, then we know that the e

We have an approximate expression of how many prime numbers there are less than N, as N gets larger. If the Riemann hypothesis is true, then we know that the errors in this approximation are nice and small, which would allow us to prove many other approximate results. (There are many results of the form "If the Riemann hypothesis is true, then...")