Goldbach's Conjecture

时间：2015-02-04 14:26:45 阅读：183 评论：0 收藏：0 [点我收藏+]

标签：

　　　　　　　　　　　　　　　　　　　　 Goldbach‘s Conjecture

Time Limit:1000MS Memory Limit:65536KB 64bit IO Format:%I64d & %I64u

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

Sample Output

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

 1 #include<iostream>
 2 #include<cstdlib>
 3 #include<cstdio>
 4 #include<cstring>
 5 #include<algorithm>
 6 #include<cmath>
 7 using namespace std;
 8 bool isprime ( int k )
 9 {
10     int t = sqrt ( k + 0.5 ) ;
11     for ( int i = 2  ; i <= t ; i ++ )
12         if ( k % i == 0 )
13             return false ;
14     return true ;
15 }
16 int main()
17 {
18  //   freopen ("a.txt" , "r" , stdin );
19     int n ;
20     while ( scanf ("%d", &n) , n )
21     {
22         int i ;
23         int t = n / 2 ;
24         for ( i = 3 ; i <= t ; i += 2 )
25             if ( isprime ( i ) && isprime ( n - i ) )
26                 break ;
27         printf ( "%d = %d + %d\n" , n , i , n - i ) ;
28     }
29     return 0;
30 }

n = isprime(i) + isprime(n - i)

Goldbach's Conjecture

标签：

原文地址：http://www.cnblogs.com/get-an-AC-everyday/p/4272108.html

踩

(0)

评论一句话评论（0）

分享档案

更多>

2021年07月29日 (22)
2021年07月28日 (40)
2021年07月27日 (32)
2021年07月26日 (79)
2021年07月23日 (29)
2021年07月22日 (30)
2021年07月21日 (42)
2021年07月20日 (16)
2021年07月19日 (90)
2021年07月16日 (35)

周排行