Prime numbers have intrigued, inspired and infuriated mathematicians for millennia, and yet mathematicians' difficulty with answering simple questions about them reveals their depth and subtlety. Join Vicky to learn about recent progress towards proving the famous Twin Primes Conjecture, and to hear the very different ways in which these breakthroughs have been made - a solo mathematician working in isolation, a young mathematician displaying creativity at the start of a career, a large collaboration that reveals much about how mathematicians go about their work.