Teach-Primary-Issue-19.7

The seemingly simple idea of prime numbers can have a profound impact on mathematical learning, says Kieran Mackle ... P rime numbers are fascinating, not only because of the roles they play in the world around us, but also because of the position they occupy in the broader story of mathematics itself. At first glance, primes may seem little more than a list to be memorised: numbers up to 100, identified and stored. But that perception conceals their deeper significance. Prime numbers offer a striking example of how seemingly simple knowledge can carry profound implications. A meaningful exploration of prime numbers in the classroom should attend to three key aspects. First, the hinterland – the historical and conceptual narrative that surrounds them. Second, their definition and the properties that follow. Third, the representations that help pupils build conceptual understanding. Weaving these threads together supports children in developing knowledge that starts in primary, but resonates throughout their entire mathematical journey. The story Like so much of mathematics, the story of prime numbers begins long before formal definitions were established. Ancient civilisations such as Babylonia and Egypt certainly worked with number systems capable of recognising indivisibility, yet no surviving evidence shows a formal concept of prime numbers. That recognition, as far as we know, begins with Euclid. In Elements , written around 300 BCE, Euclid offered two enduring insights: a definition of prime numbers and a proof that there are infinitely many of them. His proof, by contradiction, is an elegant piece of reasoning that still underpins mathematical thought. Not long after, Eratosthenes developed his sieve. This is a systematic method for identifying prime numbers, and it remains a fixture in classrooms today ( tinyurl. com/tp-Sieve ). The study of primes continued through the centuries, from India to Islamic scholars, through European thinkers such as Fermat, Euler, and Gauss, and into the modern age with Riemann and analytic number theory. But the significance of primes is not just historical or theoretical. One of their most important contemporary applications lies in cryptography. Encryption methods rely on the fact that it is easy to multiply two large primes, but extremely difficult to reverse the process and break such a product down into its prime factors. This asymmetry underpins the security of our digital systems. The study of primes, begun in antiquity, now lies at the heart of the internet. Not just a classroom CURIOSITY “The study of primes, begun in antiquity, now lies at the heart of the internet” www.teachwire.net | 61 MA THS S P E C I A L