Computers and the Riemann Hypothesis

The Riemann Hypothesis (RH) is perhaps the most important open problem in mathematics. Extensive computations have been done on it, starting with the calculations of Riemann that may have led to the formulation of the RH, and culminating in the recent verification of the RH for the first 1 1/2 billion zeros of the zeta function. 

Other computations have been made to test other hypothesis that go even beyond the RH and relate the distribution of zeros to the random matrix theories of high energy physics. These computations, as well as the methods that have been used to carry them out (as well as new ones that might lead to much more efficient calculations) will be described.