Small correction:
Goldbach's conjecture says that every
even number greater than 2 can be expressed as the sum of two
prime numbers. 2, of course,
cannot be expressed as the sum of 2 prime numbers. (See also
1 is not prime)
Stated in 1742 in a letter written by Christian Goldbach to Leonard Euler, this is one of the most difficult problems in mathematics today. In fact, the conjecture has probably replaced Fermat's Last Theorem as the most popular example of a mathematical problem that is easily understood, but difficult to solve. If you can prove, disprove, or show that this conjecture is undecidable, you will get a million dollars from Faber and Faber.