Welcome to the Sieve of Eratosthenes page.

On this page, we will tell you a little about Eratosthenes, and describe how his sieve works to help find prime numbers.

There is also our prime number calculator which uses the sieving method to find primes up to any given amount less than a million.

Eratosthenes was a Greek mathematician (as well as being a poet, an astronomer and musician) who lived from about 276BC to 194BC.

He was one of those all-round thinkers who excelled across a wide sphere of disciplines.

One of his greatest achievements was being able to calculate the circumference of the Earth. Another of his achievements was developing a method for finding prime numbers using the so-called 'Sieve of Eratosthenes'.

As a historian, he also developed chronography of the world dating from the siege of Troy.

He also studied Geography, and looked at why the River Nile flooded in certain places.

For more information about his life, use the link below.

Eratosthenes - wikipedia entryThe Sieve of Erastosthenes is a method for finding what is a prime numbers between 2 and any given number.

Basically his sieve worked in this way...

You start at number 2 and write down all the numbers from 2 upwards that you want to test.

So if you wanted to find all the prime numbers to 100, you would write down all the numbers from 2 to 100 to start off in the 'sieve'.

Once you have written down your list, the sieve works in this way...

The Sieve of Eratostenes

Step 1) Circle the first number (which is number 2). This number is prime.

Step 2) Cross out all the multiples of the number on your list. You would cross out the numbers 4, 6, 8, 10, 12, ...

These numbers have been 'sieved' out.

Step 3) Circle the next number on your list that has not been sieved out. (Number 3). This number is prime.

Step 4) Cross out all the multiples of 3 on your list.

Repeat this process until all the numbers on your list are either circled or crossed out.

The numbers circled are prime. The numbers crossed out are composite (or non-primes).

The worksheets below will help you to explore how the sieve of Eratosthenes works with numbers to 100, 150 or 200.

This calculator uses the Sieve of Eratosthenes to calculate the prime numbers from and to any given numbers under a million.

Try it and see!

Input any value into our Find Prime Numbers Calculator and it will find all the primes up to and including your value.

You can then take this information and copy and paste it somewhere else if you wish!

Prime Numbers Calculator Output

Take a look at our Prime Number page which clearly describes what a prime numbers is and what they are not.

There are also many different questions about prime numbers answered, as well as information about the density of primes.

On our Prime Number Charts page, we have many printable lists of prime numbers.

You can find the first 100 prime numbers, or print out a list of all prime numbers below 10,000.

We also have a prime number calculator which will find all the primes in a range that you set, and also a prime number tester which gives all the factors of a number, and tells you whether it is prime or not.

How to Print or Save these sheets

Need help with printing or saving?

Follow these 3 easy steps to get your worksheets printed out perfectly!

How to Print or Save these sheets

Need help with printing or saving?

Follow these 3 easy steps to get your worksheets printed out perfectly!

Math-Salamanders.com

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.

Search here!

Looking for some fun printable math games?

We have some great games for you to play in our Math Games e-books!

- Online Times Table Practice
- Online + and - Practice
- Times Table Worksheets
- Geometry Sheets
- Fraction Sheets
- Money Sheets
- Math Games
- Fun Math Puzzles & Activities
- Math Help Pages
- Math Word Problems

Have a look at some of our most popular pages to see different Math activities and ideas you could use with your child

- List of Geometric Shapes
- Equivalent Fractions
- Printable Shapes
- 3d Geometric Shapes
- Perimeter Worksheets
- Reverse Percentage Calculator

Looking for a new direction in your life?

Got a hobby or passion you want to share?

Looking to get a better work-life balance?

Create your own business from the comfort of your home...

Click here for my story!

These challenges are a great way to extend more able mathematicians and develop thinking and problem solving skills.

- 1st Grade Math Challenges
- 2nd Grade Math Challenges
- 3rd Grade Math Challenges
- 4th Grade Math Challenges
- 5th Grade Math Challenges

If you are a regular user of our site and appreciate what we do, please consider making a small donation to help us with our costs.

Get a free sample copy of our Math Salamanders Dice Games book with each donation!

Looking for some cool math certificates to hand out?

A certificate is a great way to praise achievement in math learning.

Check out our printable math certificate collection!

## New! Comments

Have your say about the Math resources on this page! Leave me a comment in the box below.