Goldbach’s Conjecture was first proposed in a weak form by Christian Goldbach in the 18th century and then in a stronger form by Leonhard Euler. It says that every odd number can be broken up into a sum of, at most, 3 prime numbers.
35 = 19 + 13 + 3
21 = 3 + 7 + 11
It has not been proven so far, but the young Terence Tao seems to be making progress.