 Extending the ideas of Riemann, two proofs of the asymptotic law of the distribution of prime numbers were obtained independently by Jacques Hadamard and Charles Jean de la Vallée Poussin and appeared in the same year (1896).Both proofs used methods from complex analysis, establishing as a main step of the proof that the Riemann zeta function is non-zero for all complex values of the variable that have the form with .During the 20th century, the theorem of Hadamard and de la Vallée Poussin also became known as the Prime Number Theorem.