Sieve of Eratosthenes

The Sieve of Eratosthenes is an method for efficiently finding all prime numbers up to a number, 120 in this case, by eliminating (colouring in) all multiples of successive primes. It uses the common optimisation of starting at p2 for each prime p, as all non-primes (composites) up to p2 were found in previous passes. Because of this it needs only consider primes up to 7, because the square of the next prime 11 is 121, larger than any number here.

A Tweet from @davidwees this morning brought this image to my attention.  I found its source on this Wikipedia page. The Sieve of Eratosthenes is a simple algorithm that finds the prime numbers up to a given integer. (If you need to brush up on prime numbers, see this definition of prime number.)

"Eratosthenes (276-194 B.C.) was the third librarian of the famous library in Alexandria and an outstanding scholar all around. He is remembered by his measurement of the circumference of the Earth, estimates of the distances to the sun and the moon, and, in mathematics, for the invention of an algorithm for collecting prime numbers. The algorithm is known as the Sieve of Eratosthenes." (Source)