Puzzles
Can every even number be written as two primes added together?
In 1742, Christian Goldbach wrote to Leonhard Euler with a simple claim: every even number greater than 2 is the sum of two prime numbers (4=2+2, 8=3+5, 100=3+97). Every even number ever checked — into the quintillions — obeys it. Can you prove it has to hold for every even number there is?
Reveal the answer
Nobody has, in nearly 300 years of trying. It's one of the oldest unsolved problems in mathematics — verified by computer for even numbers up to at least 4×10^18, but a general proof has eluded every mathematician who has attempted it, including Euler himself.
— Christian Goldbach, Letter to Leonhard Euler — 7 June 1742