The Prime Numbers plays a key role in several routines in information technology, such as public-key cryptography, which relies on the difficulty of factoring large numbers into their prime factors. Keeping in mind these important applications, is necessary that every person related to these fields to know at least one algorithm to get a set of them. The sieve of Eratosthenes is a ancient algorithm for finding all prime numbers up to any given limit, it relies on the on the idea of constant difference between an integer and its multiples. Along to get know this algorithm, the main purpose of this project is to expose the advantages of the parallel computing compared versus a sequential approach and all the applications and implications that it has.