1. Number
iGCSE (2021 Edition)
Investigation - The sieve of Eratosthenes
Lesson
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
- Start by eliminating 1, as it is not a prime number and it is not a composite number.
- Circle the next number along (which is 2). Then cross out all multiples of that number - none of these are prime.
- 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?
Did you know?
Eratosthenes was an ancient philosopher and mathematician who lived more than 2000 years ago. He developed this method of finding prime numbers, and made many other contributions to science and mathematics - including measuring the circumference of the Earth!
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
- Start by eliminating 1, as it is not a prime number and it is not a composite number.
- Circle the next number along (which is 2). Then cross out all multiples of that number - none of these are prime.
- 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?
Did you know?
Eratosthenes was an ancient philosopher and mathematician who lived more than 2000 years ago. He developed this method of finding prime numbers, and made many other contributions to science and mathematics - including measuring the circumference of the Earth!