A hipótese de Riemann e a ameaça a criptografia

Abstract

Prime numbers hide an enigma that many scholars in the field have been trying to elucidate for more than 2,300 years when the Greek Euclid showed the existence of na infinite number of these numbers. From pre-existing formulas we can generally represent any even, odd, perfect square number. However, we cannot generalize the prime numbers. Obtaining a mathematical equation capable of predicting the next prime numbers at infinity seems like a lot of work. Many attempts have already been made in the search to generalize this mysterious set, in 1859, the German Bernhard Riemann discovered a connection between prime numbers and formulated a mathematical function known as Riemann’s Zeta. The Riemann hypothesis is based on this function. It is a conjecture that if solved can describe how prime numbers are distributed at infinity. However, the discovery of this pattern could seriously compromise our interconnected world, as the basis of cryptography remains due to our lack of knowledge regarding the distribution of prime numbers at infinity.