In the talk, we present the history of Mersenne primes from the ancient Greeks to our days. We show that only strong and long-standing interactions of mathematics, computer science and computer technology made it possible to find Mersenne primes with several millions of digits. The long history divided naturally into shorter or longer epochs; before the Lucas test; the Lucas test with hand calculation; the Lucas test with early electronic computers; the epoch of supercomputers; distributed computation, the industrialisation for the search of Mersenne primes. At the end, I will speculate about the future of this game.