2262 Goldbach's Conjecture

Goldbach's Conjecture

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 31561		Accepted: 12165

Description

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.

For example: 
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. 

Input

The input 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.

Output

For each test case, print one line of the form n = a + b, where a and 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."

Sample Input

8
20
42
0

Sample Output

8 = 3 + 5
20 = 3 + 17
42 = 5 + 37

Source

Ulm Local 1998

一开始计算出1000000以内的所以素数，大约5-6万个的样子，然后查表。提交一直是TLE！！！

后来看到别人说直接计算更快？！！然后改成直接计算而不是查表，通过。

教训：并不是任何时候都适合查表。这里第一个数一般很小，随即测试了几个，小的素数都不大于1000，然后直接差后判断另外一个是不是素数就行了。而查表，即使是二分查找，也很费事。可能主要时间浪费在内存读取上（使用全局数组）。