POJ 2262 Goldbach's Conjecture

题目链接：http://poj.org/problem?id=2262

Goldbach's Conjecture

Time Limit: 1000MS
Memory Limit: 65536KTotal Submissions: 43115
Accepted: 16490

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

820420

Sample Output

8 = 3 + 520 = 3 + 1742 = 5 + 37

Source

Ulm Local 1998

思路：水题，数据不大，暴力枚举一下就好了。详见代码。

附上AC代码：

#include <cstdio>#include <cmath>//#pragma comment(linker, "/STACK:102400000, 102400000")using namespace std;int n;bool is_prime(int x){if (x==0 || x==1)return false;int t = (int)sqrt(x+0.5);for (int i=2; i<=t; ++i)if (x%i == 0)return false;return true;}int main(){#ifdef LOCALfreopen("input.txt", "r", stdin);freopen("output.txt", "w", stdout);#endifwhile (~scanf("%d", &n) && n){int t = n>>1;bool ok = true;for (int i=3; i<=t; i+=2)if (is_prime(i) && is_prime(n-i)){printf("%d = %d + %d\n", n, i, n-i);ok = false;break;}if (ok)printf("Goldbach's conjecture is wrong.\n");}return 0;}