Sieve of Eratosthenes

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.

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Who was Erastosthenes

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 entry

Sieve of Erastosthenes - how it works

The 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.

Sieve of Erastosthenes worksheets

Find Prime Numbers Calculator

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

Prime Numbers Calculator Output


Want to find out more about primes?

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.

Prime Number Charts

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.

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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.

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