Goldbach`s Conjecture

Description

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

#include<stdio.h>
#include<string.h>
bool b[10000005]={0};//不能是int
int a[1000005]={0};
void init()
{
int i,j;
for(i=2;i<=10000003;i++)
{
if(!b[i])
for(j=i+i;j<=10000003;j+=i)
b[j]=1;
}
j=1;
for(i=2;i<=10000003;i++)
if(b[i]==0)
a[j++]=i;
}
int main()
{
int i,j,m,n,ca=1,t;
init();
scanf("%d",&t);
while(t--)
{
scanf("%d",&n);
m=0;
for(i=1;i<=1000002;i++)
{
if(a[i]>n/2)break;
if(b[n-a[i]]==0)m++;
}
printf("Case %d: %d\n",ca++,m);
}
return 0;
}