# Prime Numbers using the Sieve of Eratosthenes (May 19th thru May 24th)

In ancient Greece around 250BC, Eratosthenes, a Greek mathematician devised a simple way of finding primes under 10 million. He would simply eliminate all of the numbers that were not prime, starting with 1. Then he would cirlce the first prime (2) and then cross out all of the even numbers or multiples of the prime he circled. Then he would circle the next prime (3) and cross out all of its multiples (of course, half of the multiples of 3 would already be crossed out since they were also multiples of 2). He would then move to 5, and so on.

At the end, you would have all of the prime numbers up to a given integer. The younger mathletes did this exercise on a grid of 10x10 up to 100 and found the first 25 prime numbers. The older mathletes used a grid of 20x20 up to 100 and found the first 78 prime numbers.

Prime numbers have only two factors, 1 and the number itself. The fact that 1 is not prime is of much controversy, but the best explanation is that a square number cannot also be prime.

This exercise not only teaches prime numbers but also teaches multiplication with finding multiples, addition, and division. The real fun is finding patterns in the multiples. For example, the Mathletes found in the 20x20 grid that all multiples of 7 went diagonally down and to the right where all multiples of 19 went diagonally down and to the left; multiples of 3 were a knights move down and to the left, and so on.

In mathematics, the **Sieve of Eratosthenes** (Greek: κÏŒσκινον á¼˜ρατοσθÎνους) is a simple, ancient algorithm for finding allprime numbers up to a specified integer.^{[1]} It works efficiently for the smaller primes (below 10 million).^{[2]} It was created byEratosthenes, an ancient Greek mathematician. However, none of his mathematical works survived - the sieve was described and attributed to Eratosthenes in the *Introduction to Arithmetic* byNicomachus.^{[3]}

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