Off-the-shelf Masterclass: Patterns in Primes

Off-the-shelf Primary Mathematics Masterclass about prime numbers and the patterns they hold.

Investigate the random nature of primes and the unusual patterns that emerge as you delve into them. Use a special number sieving technique to identify primes in large number grids.

  • Credit: Alicja via Pixabay

About this Masterclass

Prime numbers, and their random nature, are fascinating to lots of people from school children to experts. In fact, research into this field by mathematicians is still very active. This Masterclass was inspired by mathematician Dr Vicky Neale, and her book 'Closing the Gap' charting the on-going quest of researchers to better understand prime numbers.

Through the activities in this session and watching a clip from Vicky Neale's 'Closing the Gap' video, students are able to delve more deeply into primes. Their exploration involves simple activities with factor numbers and more complex challenges to generalise properties of prime numbers (and maybe even an attempt to predict primes!). Using the Sieve of Eratosthenes, they identify primes in large number grids and are finally shown the applications for prime number research in the field of cryptography.

With questions presented in this workshop verging on the philosophical at times, presenters navigate these with ease using the solution sheets for each worksheet and the handy speaker notes.

Length: 2 hours (see the session leader notes for ideas on how to shorten the Masterclass).

Resources needed

  • Access to YouTube to play Vicky Neale's video Closing the Gap and Marcus de Sautoy's video Prime numbers make the internet safer
  • Copies of worksheets, as detailed in Session Leader Notes 
  • Multilink cubes (approx. 100 cubes per number square worksheet, but activity can work with fewer if needed - see Session Leader Notes for details)
  • Pencils (ideally coloured) for working with the number grids
  • Optional: Print student takeaway with guidance for extension activities
  • Computer and data projector
  • Further details of quantities etc. can be found in Session Leader Notes


All supporting notes, worksheets and solutions can be downloaded from this page along with the Powerpoint presentation.

The Session Leader Notes offer full notes on the activities and a detailed list of resources, including quantities needed. 

The Session Helper Notes can be distributed amongst helpers giving them an overview of the subject and activities planned.

Ask the Ri

You can collect any student questions and email them to the Ri Masterclass team at - we will endeavour to answer them before the next Masterclass in your series.

Masterclass series support

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