THE RIEMANN HYPOTHESIS
THE RIEMANN HYPOTHESIS
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 prime numbers, 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 the Riemann Zeta function. The Riemann hypothesis asserts that all
interesting solutions of the equation
z(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.
Mathematical Description
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