The Sieve of Eratosthenes

Eratosthenes (275-194 B.C., Greece) devised a "sieve" to discover prime numbers. A sieve is like a strainer that you drain spaghetti through when it is done cooking. The water drains out, leaving your spaghetti behind. Eratosthenes's sieve drains out composite numbers and leaves prime numbers behind.

To use the sieve of Eratosthenes to find the prime numbers up to 120, make a chart of the first one hundred twenty positive integers:

• Cross out 1, because it is not prime.


• Circle 2, because it is the smallest positive even prime. Now cross out every multiple of 2; in other words, cross out every second number.


• Circle 3, the next prime. Then cross out all of the multiples of 3; in other words, every third number. Some, like 6, may have already been crossed out because they are multiples of 2.

• Circle the next open number, 5. Now cross out all of the multiples of 5, or every 5th number.


• Continue doing this until all the numbers through 100 have either been circled or crossed out. You have just circled all the prime numbers from 1 to 120!