With this procedure we find

primes numbers ??up to a number.

**Eratosthenes of Cirene (276-194 A.C.)** was a Greek scholar who lived about **two hundred years ago** and invented a method to find the **prime numbers** less than n (while useful for any given number)

It’s just a **list or tab** where appear the first n numbers and **crossed** with the **not prime** numbers:

**PROCEDURE**

1.Write all numbers are written in order up to n

2.Cross out the multiples of 2 {4,6,8,10,12,14,16….} (In the picture the 2 it’s not crossed but is included like a prime)

3.Search **next uncrossed number** (3 in this case)

4.**Cross out** the **multiples** of this number

5.While can keep crossing **return to step 3**

The **uncrossed** numbers are **the prime numbers up to n**. In the picture primes up to 120.

This is a simple method to obtain the ** first n prime numbers **. Although require store the numbers, with some possible optimizations like not store multiples of 2, 3 or 5.