（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?

#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