In this half-term Aftermaths episode, Jon and Becky take a deep dive into prime numbers and discover that they are far more than a Year 5 objective about “numbers with exactly two factors”.

The conversation begins in the classroom, exploring how we define prime numbers and why 1 and 2 are both special cases. They reflect on how primes frustrate our desire for neat patterns, how children often assume odd numbers are prime, and how the Sieve of Eratosthenes gives us a beautifully systematic way of uncovering them.

From there, the episode takes a historical journey. Jon revisits the work of Euclid, who proved over 2,000 years ago that there are infinitely many prime numbers. The discussion touches on the mind-bending nature of infinity and how powerful it is to share with pupils that maths is still unfinished.

They then explore the work of Eratosthenes, whose famous sieve remains one of the most elegant algorithms for identifying primes. Along the way, Becky shares her fondness for teaching prime factorisation and even introduces her favourite palindromic prime.

The episode moves into the 19th century and the still-unsolved Bernhard Riemann hypothesis about the distribution of primes, one of the great Millennium Prize Problems. Yes, there really is a million dollars waiting for someone who can crack it.

Finally, the discussion lands firmly in the modern world. Prime numbers underpin the encryption systems that keep online banking, shopping and government communication secure. The episode introduces RSA encryption, developed by Ron Rivest, Adi Shamir and Leonard Adleman, and explains why multiplying large primes is easy but reversing the process is extraordinarily difficult.

Key themes in this episode include:

• Why prime numbers are the “atoms” of arithmetic

• The Fundamental Theorem of Arithmetic and prime factorisation

• Infinity as a classroom conversation starter

• The beauty and mystery of unsolved problems

• How prime numbers quietly protect our digital lives

This episode is a reminder that even the most familiar Key Stage 2 content can open doors to big ideas, rich history and genuine mathematical mystery.

If you enjoyed this deep dive, leave a rating or review and let us know what topic you would like explored in a future Aftermaths episode. There are still plenty of mathematical rabbit holes to fall down.

And if you’re listening over half term, we hope you’ve had at least a little rest.