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Primitives represents numbers in terms of their prime factors, offering unusual insights into their structure. Numbers are presented as nested sets of small black dots. Three is presented as a blue circle enclosing three dots; a ‘set of three’. Six is presented as a set of three sets of two dots, or as a set of two sets of three dots.

Launch Primitives


When a number has many different prime factors, such as 30 = 3·2·5, the factors can be rearranged to offer different images of the same number.

Primitives is tailored for classroom use and perfectly suited for use with an interactive whiteboard. Hopefully older primary students and secondary students will find this application interesting.

Primitives is companion software to an article published in March 2008’s Mathematics Teacher Magazine.



Posters based on the Primitives software are now available from the ATM online shop.

Grid primitives combines the ‘Primitive’ visualisations with the Sieve of Eratosthenes. The Primitive visualisations of the first 42 numbers are arranged into a six column grid that is often used when finding prime numbers by elimination using the Sieve of Eratosthenes algorithm. Click on the image or here for a larger image.

The visualisations are reduced in size to conform to the size of the grid, and behind them the pattern of multiples of 2, 3, 5 and 7 are each highlighted in the colour corresponding to the respective prime number. The prime numbers are particularly highlighted by an 11-pointed star behind each one.

The choice of a six column structure may lead students to question why after the bottom row, primes only appear in the first and fifth columns, or to put it mathematically, why all primes other than 2 and 3 are in the pattern 6n±1, where n is a positive integer, but that not all such numbers are prime. In each column, 25 and 35 disrupt the apparent pattern of primes. Studying this may lead students to futher questions about prime numbers for further study.


  1. March 10, 2008

    A stunningly simple idea, beautifully realised.

  2. nicola batey #
    March 10, 2008

    As a secondary maths teacher I was wondering if it was possible to buy the primitives grid poster anywhere?

    • February 10, 2010


      This is a long time to reply to your original question. I have only just reviewed these comments, as I'm not really working in the education industry any more. The primtives posters are available:

      Regards, Alec

  3. malcolm bellamy #
    May 13, 2009

    Wonderful. This is, as you say, a really good way to get children to appreciate the beauty of mathematics as well as allowing them to investigate factors and primes. The key is colour and representation of number in patterns.
    Congratulations. I look forward to seeing the revised and finished version.

  4. November 25, 2009

    A stunningly simple idea, beautifully realised.

  5. B Kissane #
    July 15, 2011

    Is Primitives still available? Links don’t seem to work.

    • July 15, 2011

      Sorry about that. I have just changed host, and had to reinstall WordPress. Some of my settings have been lost. You can currently find the Primives Application using this link:

  6. Pittske #
    August 27, 2013

    Thanks very much It’s fine now – works a treat! I will head off and buy some posters from ATM!

  7. Fabiana Miranda #
    January 19, 2018

    Hello, I’m a teacher in Rio de Janeiro and I really enjoyed your software primitives. But I have quest to indicate to some colleagues and no longer meet, not even to buy.
    Could you make it available?

    • January 20, 2018

      Hi! Primitives is still here, but many browsers don’t allow Flash anymore. I’ve started to build Primitives in HTML5 here: It’s not the same, but perhaps it will help?

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  1. Primitives Article |
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  3. Numbers – Visualisations | Mathematics, Learning and Technology

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