Riemann conjectured that all nontrivial zeros of the zeta function  have real part equal to  In spite of all the efforts this conjecture, called Riemann hypothesis, was not demonstrated still at the moment. The Riemann hypothesis (denoted by RH) is a mathematical conjecture which states that the nontrivial Riemann zeta function has zeros such that all the values lie on the critical line. This hypothesis also implies the results of the distribution of prime numbers which are very important in mathematics.

This expository paper is devoted to basic facts about Riemann hypothesis, following to some extent the historical development of the problem.

history, zeta function, Riemann hypothesis, general Riemann hypothesis.