 An important paper concerning the distribution of prime numbers was Riemann's 1859 memoir "On the Number of Primes Less Than a Given Magnitude", the only paper he ever wrote on the subject.Riemann introduced new ideas into the subject, the chief of them being that the distribution of prime numbers is intimately connected with the zeros of the analytically extended Riemann zeta function of a complex variable.In particular, it is in this paper of Riemann that the idea to apply methods of complex analysis to the study of the real function originates.