Goldbach's Conjecture（哥德巴赫猜想）

Goldbach's Conjecture

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 5277    Accepted Submission(s):
2022

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Problem Description

Goldbach's Conjecture: For any even number n greater
than or equal to 4, there exists at least one pair of prime numbers p1 and p2
such that n = p1 + p2.
This conjecture has not been proved nor refused yet.
No one is sure whether this conjecture actually holds. However, one can find
such a pair of prime numbers, if any, for a given even number. The problem here
is to write a program that reports the number of all the pairs of prime numbers
satisfying the condition in the conjecture for a given even number.

A
sequence of even numbers is given as input. Corresponding to each number, the
program should output the number of pairs mentioned above. Notice that we are
interested in the number of essentially different pairs and therefore you should
not count (p1, p2) and (p2, p1) separately as two different pairs.

 

Input

An integer is given in each input line. You may assume
that each integer is even, and is greater than or equal to 4 and less than 2^15.
The end of the input is indicated by a number 0.

 

Output

Each output line should contain an integer number. No
other characters should appear in the output.

 

Sample Input

6

10

12

0

 

Sample Output

1

2

1

 #include <iostream>
 using namespace std;
 int a[];
 int isprime()
 {
     int i,k,x;
     for(i=;i<;i++)
     {
         for(k=;k<=i/;k++)
         {
             if(i%k==)
                 break;
         }
         if(k==i/+)
             a[i]=;
         else
             a[i]=;
     }
     return ;
 }
 int main()
 {
     int x,i,j,count=;
     isprime();
     while(cin>>x&&x)
     {
         count=;
         for(i=j=x/;i>=;i--,j++)
         {
             if(a[i]&&a[j])
             {
                 count++;
             }
         }
         cout<<count<<endl;
     }
 }