.Clay
Mathematics Institute |

## The Riemann Hypothesis |
## millennium prize problems / the riemann hypothesis problem |

Some numbers have the special property that they cannot be expressed as the product of two smaller numbers, e.g., 2, 3, 5, 7, etc. Such numbers are called

primenumbers, and they play an important role, both in pure mathematics and its applications. The distribution of such prime numbers among all natural numbers does not follow any regular pattern, however the German mathematician G.F.B. Riemann (1826 – 1866) observed that the frequency of prime numbers is very closely related to the behavior of an elaborate function “z(s)” called theRiemann Zeta function. The Riemann hypothesis asserts that allinterestingsolutions of the equationz(s) = 0

lie on a straight line. This has been checked for the first 1,500,000,000 solutions. A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers.