Sieve of Eratosthenes, << ehr uh TOS thuh neez, >> is a method developed in the 200’s B.C. by the Greek mathematician Eratosthenes for identifying prime numbers. These are whole numbers other than 1 that can be divided evenly by only 1 and themselves. Today, mathematicians use computers to identify prime numbers. But Eratosthenes’s method, though much slower, always works.
To find prime numbers with the sieve of Eratosthenes, first write the series of whole numbers starting with 2. Cross out every second number after 2. This eliminates all numbers that can be divided evenly by 2, except for 2 itself. Similarly, cross out every third number after 3. (Include those numbers that you have already crossed out.) This step eliminates all the numbers that can be divided evenly by 3, except for 3 itself.
Then, since 4 is already crossed out, move on to 5. Cross out every fifth number after 5. Continue this process for multiples of 7, and so on. Numbers that are not crossed out can be thought of as having passed through a sieve (strainer) that has caught all the rest.
Any number that has not been crossed out when you start with a number to its right—for example, the 3, when you begin a crossing-out step with 6—is prime. This process is endless because, as the Greek mathematician Euclid proved about 300 B.C., there is no largest prime number.
