Investigation: The Sieve of Eratosthenes

In this investigation we will find all the prime numbers between 1 and 200.

Materials

• A pen or pencil
• A grid of all the numbers from 1 to 200, like this one:

Instructions

1. Start by eliminating 1, as it is not a prime number and it is not a composite number.
2. Circle the next number along (which is 2). Then cross out all multiples of that number - none of these are prime.
3. Repeat step 2 until you reach the end of the grid.
   
   Here is the grid after the first two numbers are circled and their multiples crossed out:

Questions

• What is the next number to be circled after 2 and 3?
• How many numbers are circled between 1 and 200 by the end of the process?
• What is special about the numbers you circled?
• What does it mean if a number is crossed out only once? What about more than once?