The Math Missus Sarah Smellie shows us how prime numbers keep our online shopping safe from cyber thieves and super spies.

Their result – that infinitely many primes can be expressed as p² + 4q², with both p and q prime – builds a bridge between classical number theory and new-age combinatorics.

Prime numbers are found hidden in nature, but humans have made spectacular use of them, writes mathematician Marcus du Sautoy.