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 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 Hilbert'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.

References

  1. http://www.claymath.org/millennium/