A method of finding all of the prime numbers less than a given number n. First, go through all the numbers from 2 to n crossing out all multiples of 2 after 2.

Next, go through all the numbers from 3 to n crossing out all multiples of 3 after 3.

Then, go through all the numbers from 5 to n crossing out all multiples of 5 after 5. Continue the process for all the prime numbers below n^{1/2}. Those numbers that remain after completing the process are all the prime numbers less than the given number n.