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The '''Riemann hypothesis''' states that the non-trivial zeros of the [[Riemann Zeta function]] function all have real component <math>\frac{1}{2}</math>. The conjecture was first proposed by [[Bernhard Riemann]] in 1859 and is considered to be the greatest unsolved problem in mathematics. The hypothesis was listed as one of the seven [[Millennium problems]] by the Clay Mathematics Institute and 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 [[pime number theorem]] is small. Alternatively, the Riemann hypothesis can be thought of as a statement that the [[prime number]]s are very smoothly distributed.   

The '''Riemann hypothesis''' states that the non-trivial zeros of the [[Riemann Zeta function]] function all have real component <math>\frac{1}{2}</math>. 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==

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[[Category:Complex analysis]]

[[Category:Complex analysis]][[