Professor Andrew Hone, Associate Member of the Institute of Cyber Security for Society (iCSS), is working with the Institute for Research in Schools (IRIS) on a new project, *Huge Primes*, which focuses on prime numbers and primality testing.

This project aims to give school students throughout the UK the opportunity to learn techniques from mathematics and cryptography that underpin the security of everyday applications, like online shopping, social media and internet banking. Participants in the project will not only be able to find out how modern cryptography works, but will also have the chance to get involved in original research. The goal is to inspire the next generation of mathematicians, computer scientists and cryptographers.

This project is about old and new ways to generate and test large prime numbers, and how these can be used in cryptography. Number theory is about the properties of whole numbers, and the different ways they combine when they are added or multiplied together. Prime numbers are basic building blocks: every whole number has a unique decomposition into prime factors, similarly to the way that a molecule of a chemical substance can be broken down into its constituent atoms.

Cryptography is the science of sending coded messages, in such a way that they can only be decoded and read by the intended recipient. It turns out that many of the most effective and commonly used methods for solving this practical problem are based on seemingly quite abstract ideas from number theory, and large prime numbers in particular.

Andrew aims to develop the web materials for this project with IRIS in the first half of 2022, so that the research can start trials and gauge interest by getting feedback from a small group of schools in the summer. Ideally, the pilot will be ready to run by September 2022, if not the full project launch. Maplesoft has agreed to sponsor the project by making free Maple licences available to all participating students.