A - 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

Note

1.      An integer is said to be prime, if it is divisible by exactly two different integers. First few primes are 2, 3, 5, 7, 11, 13, ...

#include <stdio.h>
#include <string.h>
#include <algorithm>
#define MAXN 10000005
using namespace std;

bool isprime[MAXN];
int prime[666666], tot; //防止MLE

void getPrime() {
    memset(isprime, true, sizeof(isprime));
    isprime[0] = isprime[1] = false;
    tot = 0;
    for(int i = 2; i < MAXN; i++) {
        if(isprime[i]) prime[tot++] = i;
        for(int j = 0; j < tot && prime[j] <= MAXN / i; j++) {
            isprime[i * prime[j]]=false;
            if(i % prime[j] == 0) break;
        }
    }
}

int main()
{

	int T,cas=1,n;
	scanf("%d",&T);
    getPrime();
	while(T--)
	{
		int ans=0;
		scanf("%d",&n);
		for(int i=0;prime[i]<=n/2;++i)
		{
			if(isprime[n-prime[i]]) ans++;
		}
		printf("Case %d: %d\n",cas++,ans);
	}
	return 0;
}