How many prime numbers are there not exceeding 20? There are eight of them: 2, 3, 5, 7, 11, 13, 17 and 19. How many prime numbers are there that do not exceed a million? Billion? Is there a general formula that could save us from direct recalculation? The conjecture put forward by the German mathematician Bernhard Riemann in 1859 has become an obsession for generations of scientists: elegant, intuitive and yet completely unprovable, it remains one of the great unsolved problems in modern mathematics. It is no coincidence that the Clay Institute of Mathematics included the Riemann Hypothesis among seven “Millennium Problems”, each of which has a reward of one million dollars. A popular and witty book by American mathematician and publicist John Derbyshire tells about the numerous attempts to prove (or disprove) the Riemann hypothesis over the past one hundred and fifty years, as well as the fate of people obsessed with this task.