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.
- 8 = 3 + 5. Both 3 and 5 are odd prime numbers.
- 20 = 3 + 17 = 7 + 13.
- 42 = 5 + 37 = 11 + 31 = 13 + 29 = 19 + 23.
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.
The input file will contain one or more test cases.
Each test case consists of one even integer n
with 6 ≤ n < 1000000
Input will be terminated by a value of 0 for n
For each test case, print one line of the form n = a + b
are odd primes. Numbers and operators should be
separated by exactly one blank like in the sample output below.
If there is more than one pair of
odd primes adding up to n
, choose the pair where the difference
b - a
is maximized. If there is no such pair, print a line saying
"Goldbach's conjecture is wrong."
8 = 3 + 5
20 = 3 + 17
42 = 5 + 37