Prime Numbers and the Sieve of Eratosthenes

What is a prime number? It is a number which has only two factors: 1 and itself. Think about the number 2. What two numbers and only two numbers can you multiply to get the product of 2? Only the numbers 1 and 2. What about the number 3? Again, you can only multiply two numbers to get the product of 3 , 1 x 3. Is 4 a prime number? What two numbers can you multiply with a product of 4? In this case 4 x 1 = 4, but so does 2 x 2. This means that 4 is a composite number. Composite numbers are all those numbers which have more than one set of factors. Think of a number. Remember your multiplication facts. Is the number prime or composite?

All numbers, with TWO exceptions are either prime or composite. The numbers 0 and 1 are neither prime or composite. Think about why this might be. 1 is not prime because it has only one factor. Use what you know about the 0 property of multiplication to explain why 0 cannot be prime or composite. On Looseleaf paper, write a paragraph explaining why 0 is neither prime nor composite.

It would take a long time to figure our all the prime numbers there are. Fortunately, a Greek mathematician, Eratosthenes, discovered a way to quickly determine all the prime numbers between 1 and 100. How would you figure out all the prime numbers? In a well-organized paragraph, explain your method for determining all the prime numbers between 1 and 100. Trade papers with someone else to see if s/he can follow your method and agrees with you.

Check out how well your method matches up with the traditional method that Eratosthenes developed. Click on this link Ask Dr. Math About Prime Numbers and try Eratosthenes method to figure out prime numbers. Who’s method worked better, yours or his? While your on this site, be sure to check out the link to see the largest known prime number.

For extra credit, see if you can find all the prime numbers between 101 and 200.