（Problem 46）Goldbach's other conjecture

It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.

9 = 7 + 21²
15 = 7 + 22²
21 = 3 + 23²
25 = 7 + 23²
27 = 19 + 22²
33 = 31 + 21²

It turns out that the conjecture was false.

What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?

题目大意：

Christian Goldbach 提出每个奇合数都可以写作一个质数与一个平方数的二倍之和：

9 = 7 + 21²
15 = 7 + 22²
21 = 3 + 23²
25 = 7 + 23²
27 = 19 + 22²
33 = 31 + 21²

但是这个推测是错误的。

最小的不能写作一个质数与一个平方数的二倍之和的奇合数是多少？

//（Problem 46）Goldbach's other conjecture

// Completed on Fri, 26 Jul 2013, 16:58

// Language: C11

//

// 版权所有（C）acutus   (mail: [email protected]) 

// 博客地址：http://www.cnblogs.com/acutus/

#include<stdio.h>

#include<math.h>

#include<string.h>

#include<ctype.h>

#include<stdlib.h>

#include<stdbool.h>



bool issquare(int n)  //判断一个自然数是否为一个平方数

{

    if(ceil(sqrt(n))*ceil(sqrt(n))==n) return true;

    else return false;

}



bool isprim(int n)  //素数判断

{

    for(int i=2; i*i<=n; i++)

    {

        if(n%i==0) return false;

    }

    return true;

}



bool judge(long long n)

{

    int i=1;

    long long t;

    while((t=(n-2*(i*i)))>0)

    {

        if(isprim(t)) return true;

        i++;

    }

    return false;

}



int main()

{

    for(long long i=1001; i<100000000; i=i+2)

    {

        if(!isprim(i) && !judge(i)) 

        {

            printf("%lld\n",i);

            break;

        }

    }

    return 0;

}

Answer:

5777