**Abstract. **
The prime numbers are among the most important objects of study in Number Theory. Riemann's zeta function is one of the main tools for studying the prime numbers. The prime numbers and the zeta function are connected in many ways. The first part of the talk will be a survey of some such known relationships.
The second part of the talk will be devoted to new, rather striking, ways in which the prime numbers are encoded by the zeta function. They were discovered by the speaker in the last years via intensive computer computations. So far no theoretical explanations were given to the observed phenomena. |