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Introduction

Introduction currently, primes are widely used in cryptography and digital signatures, for this would be very good to have an algorithm or a set of algorithms, capable of efficiently, generating great lengths cousins. While we have these algorithms, several problems can occur and it may happen that the prime numbers that we are generating not serve us, to do this we must consider several points. For even more opinions, read materials from Jorge Perez. We must ensure that the numbers that we are generating are really cousins or with a very high probability sufficiently. Check if a number is composite or cousin, can be treated in several ways, Ruffini, a very simple so just by showing the prime factors, we convenceriamos without having to show a complex theory or auxiliary arguments. Quite similar otherwise would find him a divider to this number, with this we opinion it easily to any person. But as persuade someone if the number is Prime, to do this we must go to auxiliary theories that will be simple or complex According to the level of strength of our algorithm, which show conditions that must meet a number to be prime or not, this way we would check them and if you met or not, we would know that he is cousin or sometimes with security compound and others with a high probability. Another feature of the numbers that we are going to generate, is that anyone can get them, even if you have knowledge of the workings of our algorithms. This can be achieved with the use of functions that generate random numbers. Once guaranteed both things, we cannot rely on the obtained primes. The problem of recognizing prime numbers in the natural, has been one of the most ancient themes and that the scientific community has been given always great effort throughout history. The sieve of Eratosthenes is the oldest method (200 B.C.) to find prime numbers, it is able to recognize the first primes up to a given number, you currently have more historical significance than practical, by its high computational cost.