AS PROPRIEDADE DOS NÚMEROS PRIMOS

In the 4th century BC, mathematicians (philosophers of the time) were already studying prime numbers. Aristotle, a Greek mathematician (384–322 BC), created the Aristotle Sieve, a property still used today to identify prime numbers. Euclid, a mathematician who lived in the 4th century BC, wrote that prime numbers are part of an infinite set (the set of prime numbers). Throughout history, several mathematicians have presented works that help in the identification of prime numbers. Those who demonstrated methods or properties that are successful in defining a given number that is prime, at any point on the numerical scale, wrote their expressions in symbols unknown to modern men, which is why such expressions fell into oblivion and were accepted as expressions that did not work in defining prime numbers. The most widely used method to define prime numbers even today is successive division, in which the divisors are prime numbers in sequence. Mathematician Christian Goldebach (1690 – 1764) presented his work entitled Goldebach's Conjecture, which proves that all even numbers  4 can be composed by the sum of two prime numbers. (Our emphasis). French mathematician Marin Mersenne (09/08/1558 – 09/01/1648) wrote that prime numbers would be the predecessors of a power of base two, (2n – 1). We proved that successors of a power of base two (2), for an even exponent n (2n + 1) and n  2, can be prime numbers. And predecessors of a power of base two (2), for an odd exponent n (2n – 1) and n > 2, can also be prime numbers.