K - Goldbach`s Conjecture

Goldbach’s conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states:

Every even integer, greater than 2, can be expressed as the sum of two primes [1].

Now your task is to check whether this conjecture holds for integers up to 107.

Input
Input starts with an integer T (≤ 300), denoting the number of test cases.

Each case starts with a line containing an integer n (4 ≤ n ≤ 107, n is even).

Output
For each case, print the case number and the number of ways you can express n as sum of two primes. To be more specific, we want to find the number of (a, b) where

1.  Both a and b are prime
   

2.  a + b = n
   

3.  a ≤ b
   

Sample Input

2
6
4

Sample Output

Case 1: 1
Case 2: 1

代码如下

#include
#include
bool prime[10000010];
int main()
{
	int i,j;
	for(i=2;i*i<=10000000;i++)
	{
		if(!prime[i])
		{
			for(j=i*i;j<=10000000;j+=i)
			prime[j]=1;
		}
	}
	int t,k=1;
	scanf("%d",&t);
	while(t--)
	{
		int n;
		long long s=0;
		scanf("%d",&n);
		for(i=2;i<=n/2;i++)
		{
			if(!(prime[i]+prime[n-i]))
			s++;
		}
		printf("Case %d: %lld\n",k++,s);
	}
	return 0;
}