UVa 543 Goldbach ' s conjecture: Primes & Goldbach conjecture

543-goldbach ' s conjecture

Time limit:3.000 seconds

Http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=24&page=show_problem &problem=484

In 1742, Christian Goldbach, a German amateur mathematician, sent a letter to Leonhard Euler of which he made the Followin G conjecture:

Every number greater than 2 can be written as the sum of three prime.

Goldbach CWAs considering 1 as a primer number, a convention that is no longer followed. Later on, Euler re-expressed the conjecture as:

Every even number greater than or equal to 4 can be expressed as the sum of two prime. 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's it is still unproven whether the conjecture are right. (Oh wait, I have the proof of course, but it are too long to write it on the margin of this page.)

Anyway, your task is now to verify Goldbach's conjecture as expressed by Euler for all even numbers less than a million.

Input

The input file would contain one or more test cases.

Each test case consists of the one even integer n with.

Input'll is 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 is separated by exactly one blank as 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 km/
0

Sample Output

8 = 3 + 5
= 3 +
42 = 5 + 37

Water problem.

Complete code:

/*0.049s*/
    
#include <cstdio>  
#include <cmath>  
const int MAXN = 1000010;  
const int m = (int) sqrt (MAXN);  
    
BOOL VIS[MAXN];  
    
inline void Cal_prime ()  
{  
    int i, J;  
    for (i = 2; I <= m. ++i)  
        if (!vis[i) for  
            (j = i * i; j < maxn; j = i)  
                vis[j] = true;  
}  
    
int main ()  
{  
    cal_prime ();  
    int n, I;  
    while (scanf ("%d", &n), N)  
    {for  
        (i = 3; i < n; ++i)  
        {  
            if (!vis[i) &&!vis[n-i]) 
  
   {  
                printf ("%d =%d +%d\n", N, I, n-i);  
                break;  
            }  
    }} return 0;  
}
  

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