Millennium Prize Problems - The Riemann Hypothesis

The Riemann Hypothesis

The Riemann hypothesis is that all nontrivial zeros of the analytical continuation of the Riemann zeta function have a real part of 1/₂. A proof or disproof of this would have far-reaching implications in number theory, especially for the distribution of prime numbers. This was Hilbert's eighth problem, and is still considered an important open problem a century later.

The official statement of the problem was given by Enrico Bombieri.