Sieve of Eratosthenes Modeling

math1


ASL

Eratosthenes was a man who lived a long time ago in Greece. He was a mathematician. His job was to think about and solve math problems. He read about math problems. He also thought about new math problems to answer. One math problem he thought about was how to find prime numbers. He wanted a way to find all of the prime numbers in a group of numbers.



ASL

A prime number is a special type of number in math. A number is prime when only 1 and itself (the number) can divide it. For example, 2 is a prime number. Only 1 and 2 can divide 2. No other number can divide 2 evenly. Another prime number is 11. Only 1 and 11 can divide 11 evenly. 11 cannot be divided by 2, 3, 4, 5, 6, 7, 8, 9, or 10. Can you think of another prime number?



ASL

If a number is not prime, then it is composite. A composite number can be divided by 1 and itself and another number. For example, 6 is a composite number. 6 can be divided by 2. Therefore, 6 cannot be prime and must be composite. Another example is 10. 1, 2, 5, and 10 can all divide 10. Since 2 and 5 can divide 10, then 10 cannot be prime. 10 is composite. Can you think of another composite number?



ASL

Eratosthenes did not want to find just one prime number. Another person had already done that. He wanted an easy way to find all the prime numbers in a group of numbers. He wanted to be sure he found every prime number, and no composite numbers.



ASL

Eratosthenes thought of a way to find these prime numbers. First, he chose his group of numbers. Then, he took out all of the composite numbers in the group. Remember, composite numbers are the opposite of prime numbers. If he took out all of the composite numbers, then only the prime numbers would be left.



ASL

Eratosthenes did not cross out the numbers randomly. He used a pattern to cross off these numbers. This pattern helped him not forget any of the composite numbers. Anyone can now use this pattern to find prime numbers. It is called the Sieve of Eratosthenes.



ASL

To use the Sieve of Eratosthenes, you need to be able to divide numbers. When one number can divide another number, it is divisible. This model will show you how to follow his pattern. Try to figure out what the pattern is as you work. If you figure it out, then you can find a prime number any time you want!


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