題目 :



在1742年一個德國業餘數學家Christian Goldbach，他作了以下的猜測：

任何一個比4大的偶數一定能夠找到2個奇數的質數使其和相等。例如：



8=3+5（3和5都是奇數，且是質數）



20=3+17=7+13



42=5+37=11+31=13+29=19+23



你的任務就是寫一個程式來驗證他的猜測。



Input



輸入包含好幾筆測試資料，每筆資料1行,包含一個偶數的整數n（4 < n < 1000000）。

n=0代表輸入結束。



Output



對每筆輸入資料你應該要以 n = a + b 的形式輸出，其中 a、b都是奇數的質數。

如果有一組以上的 a、b，請輸出 b-a 最大的那組。

如果找不到這樣的 a、b，請輸出 Goldbach s conjecture is wrong.



解法 :



1. 先建立一個一為陣列，把奇數質數的格子設為 1，其餘設為 0 ，使用埃氏篩法得到質數





2. 判斷一為陣列，如果兩個為 1 的陣列相加等於輸入，輸出陣列位置，即為答案-Title: In 1742, a German amateur mathematician Christian Goldbach, he made the following guess: Any even larger than 4 will be able to find two odd primes it and equal. For example: 8 = 3+5 (3 and 5 are odd, and is a prime number) 20 = 3+17 = 7+13 42 = 5+37 = 11+31 = 13+29 = 19+23 Your task is to write a program to verify his guess. Input pen input contains several test data, each data row that contains an even integer n (4 < n < 1000000). n = 0 represents the input end. Output for each input data you should to n = a+ b output in the form in which a, b are odd primes. If there is more than one set of a, b, ba please output the set maximum. If you can not find such a, b, please output " Goldbach' s conjecture is wrong."　Solution: 1. To set up a one array, the odd prime number grid is set to 1, and the rest is set to 0, using the sieve method to obtain Erichsen 2. judge a prime number in an array, the array is 1 if the sum of the two equal input and output array position,