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. 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.