# Difference between revisions of "Riemann hypothesis"

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− | The '''Riemann hypothesis''' states that the non-trivial zeros of the [[Riemann Zeta function]] function all have real component | + | The '''Riemann hypothesis''' states that the non-trivial zeros of the [[Riemann Zeta function]] function all have real component ½. The conjecture was first proposed by [[Bernhard Riemann]] in 1859 and is considered to be one of the greatest unsolved problem in mathematics. The hypothesis is one of [[Hilber]]'s twenty-three problems and was listed as one of the seven [[Millennium problems]] by the Clay Mathematics Institute. There is a million dollar prize for its solution.<ref>http://www.claymath.org/millennium/</ref> The statement is essentially equivalent to the claim that the error term in the [[prime number theorem]] is small. Alternatively, the Riemann hypothesis can be thought of as a statement that the [[prime number]]s are very smoothly distributed. |

==References== | ==References== |

## Revision as of 16:17, 22 July 2018

The **Riemann hypothesis** states that the non-trivial zeros of the Riemann Zeta function function all have real component ½. The conjecture was first proposed by Bernhard Riemann in 1859 and is considered to be one of the greatest unsolved problem in mathematics. The hypothesis is one of Hilber's twenty-three problems and was listed as one of the seven Millennium problems by the Clay Mathematics Institute. There is a million dollar prize for its solution.^{[1]} The statement is essentially equivalent to the claim that the error term in the prime number theorem is small. Alternatively, the Riemann hypothesis can be thought of as a statement that the prime numbers are very smoothly distributed.