The numbers are 1, 2, 3, 11 and 17. Note that, because 2 is the
only even prime, the only way we can sum two primes to give an odd
number is to sum the odd number before it (if it is a prime) and
One of the oldest unsolved problems in number theory is Goldbach's
conjecture, which says that every even number (except 2) can be
written as the sum of two primes. Perhaps you could be the first to
This problem is taken from the UKMT Mathematical Challenges.