Goldbach`s Conjecture（素筛水题）题解

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

思路：

水题一只，叫你求n=a+b且a，b都是素数这样的ab的对数。只要素筛一下，就能做了。最好先储存一下10^7以内的素数，数答案时只要到n/2就行了（因为a<=b），不知道不弄会不会超时，可以试一下。

代码：

#include
#include
#include
#include
#include
#include
#include
#include