The are several prime sieves, all of which are designed to find all of the prime numbers up to some finite limit \(n\). The sieve of Eratosthenes is an ancient algorithm, and is the one used in this applet. Begin by arranging the numbers 1 through \(n\) in a grid, with at least as many columns as rows. Starting with 2, cross off all multiples of each number \(i\) in the top row except for the \(i\) itself. The numbers that remain are all prime.