Sieve of Eratosthenes

Your first task is to click on number 1. One is not a prime number as it does not have two factors.


First task completed.
Number one has been removed.

Second task completed.
The multiples of two greater than two have been removed.

Third task completed.
The multiples of three greater than three have been removed.

Multiples of five have been removed.

Multiples of seven have been zapped.

Multiples of eleven are no more.

Goodbye multiples of thirteeen.

Asta lavista multiples of seventeen.

No more multiples of nineteen.

Adios multiples of twenty three.

Do you miss the multiples of twenty nine?

Good riddance multiples of thirty one.

Bye bye multiple of thirty seven.

Chao multiple of forty one.

The multiple of forty three has been exterminated!

Final task completed.
The one multiple of forty seven has been removed.

Well done!

There is no simple formula for generating the sequence of prime numbers but this is a method devised many years ago by the mathematician Eratosthenes of Cyrene (he also invented Geography!). It involves methodically eliminating the numbers that are know not to be prime until only the prime numbers remain. Begin by crossing out one as it is not a prime number (it does not have two factors, it is a square number). Two is a prime number but all of its multiples a not (they are composite numbers) so cross out all of the multiples of two but leave two as the first prime number. Next cross out all of the multiples of three except three itself. The number four and all of its multiples have already been crossed out as they are also multiples of two. Next cross out all the multiples of five except five itself. Continue this process until you have discovered as many prime numbers as you need.

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Extension Activities

  1. Which number was clicked on the greatest number of times while doing this activity? Why?
  2. Make a plan for extending this task to find all prime numbers up to 200. Minimise the work you will need to do!
  3. Try doing this task with number grids of different dimensions. You can do it online by visiting the Number Grid page.
Other Number Grids
A partly complete Sieve of Eratosthenes on a 14-column number grid.



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