Erastosthenes's sieve for prime numbers. Diagram showing a method for identifying prime numbers, described by the Ancient Greek mathematician Eratosthenes (276 BC-194 BC). The method involves eliminating all multiples of prime numbers as they are discovered. Here, the multiples of two, the first prime number, have already been eliminated, and the sieve has been applied to the set of odd numbers from 1 to 359. The next prime number, 3, is identified and its multiples eliminated (green lines). This leaves 5 as the next prime number, and its multplies are eliminated (pink). This is repeated for 7 (blue), 11 (orange), 13 (red) and 17 (purple). The remaining numbers are all prime numbers (eg. 19, 23 ... 353, 359), with 359 being the 72nd prime number.