Perfect numbers and Mersenne primes might seem like unrelated branches of math, but work by Euclid and Euler over 2000 years apart showed they are so deeply connected that a one-to-one correspondence exists between the even perfect numbers and the Mersenne primes. The existence of odd perfect numbers remains and unsolved problem. Produced by Tom Rocks Maths intern Kai Laddiman, with assistance from Dr Tom Crawford. Thanks to St John's College, Oxford for funding the placement. If you are interested in working with Tom on a project get in touch via https://tomrocksmaths.com/contact/ All work produced by TRM interns can be found here: https://tomrocksmaths.com/interns/ For more maths related fun check out Tom's website https://tomrocksmaths.com/ Follow Tom on Facebook, Twitter and Instagram @tomrocksmaths https://www.facebook.com/tomrocksmaths/ https://twitter.com/tomrocksmaths/ https://www.instagram.com/tomrocksmaths/ Get your Tom Rocks Maths merchandise here: https://beautifulequations.net/collections/tom-rocks-maths