Oito testes de primalidade

Abstract

Since prime time the prime numbers have been the basis of great mathematical problems, many of these problems have crossed centuries without anyone being able to solve them, is the case of the famous Goldbach conjecture that says that even numbers greater than 2 can be written as the sum of two prime numbers, and the conjecture of the twin cousins ​​which states that there are infinite pairs of twin cousins, these affirmations have not yet been demonstrated. But a question is unavoidable when it comes to prime numbers: how to recognize them? To this day, no method is known. efficient enough to prove that any number is prime or not, and that directly influences the difficulty in proving or refuting conjectures about numbers cousins Although not very efficient, there are several tests to recognize if certain numbers are prime, these are known as primality tests and many of these conditions, which are useful only for particular numbers. In this paper we will present some of these primality tests with their statements and any theoretical basis required to carry them out. Applications of these tests will also be presented in the verification of the primality of some numbers.