In 1742, Christian Goldbach, a German amateur mathematician, sent a letter to Leonhard Euler in which he made the following conjecture:
Every even number greater than 4 can be
written as the sum of two odd prime numbers.
Today it is still unproven whether the conjecture is right. (Oh wait, I have the proof of course, but it is too long to write it on the margin of this page.)
Anyway, your task is now to verify Goldbach's conjecture for all even numbers less than a million.
Each test case consists of one even integer n with .
Input will be terminated by a value of 0 for n.
If there is no such pair, print a line saying ``Goldbach's conjecture is wrong."
8 20 42 0
8 = 3 + 5 20 = 3 + 17 42 = 5 + 37