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 + 2×1²
15 = 7 + 2×2²
21 = 3 + 2×3²
25 = 7 + 2×3²
27 = 19 + 2×2²
33 = 31 + 2×1²

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 <iostream>
#include <vector>
#include <iterator>
#include <cmath>

using namespace std;

class PE0046
{
private:
    static const int m_max = 1000000; // one million
    bool
 
 checkPrime(int number);
    bool validateGoldbachOtherConjecture(int number, vector<int>& primes_v);

public:
    int findSmallestOddComposite();
};

bool PE0046::checkPrime(int number)
{
    if (number%2 == 0 && number>2 || number < 2)
    {
        return false;
    }

    double
 
 squareRoot=sqrt((double)number);

    for(int i=3;i<=(int)squareRoot;i+=2)  // 3, 5, 7, ...(int)squareRoot
    {
        if (number % i == 0)
        {
            return false;
        }
    }

    return true;
}

bool PE0046::validateGoldbachOtherConjecture(int number, vector<int>& primes_v)
{
    vector<int>::reverse_iterator iter=primes_v.rbegin();
    int prime;
    int diff;

    while (iter != primes_v.rend())
    {
        prime = *iter;
        
        diff = number - prime;

        if (0 == diff % 2)
        {
            int root = (int)sqrt((double)diff/2.0);
            if (diff == 2*root*root)  // number = prime + 2*root*root
            {
#ifdef UNIT_TEST
                cout << number << " = " << prime << " + 2 x "<<root<<"^2"<<endl; 
#endif
                return true;
            }
        }
        iter++;
    }
    return false;
}

int PE0046::findSmallestOddComposite()
{
    vector<int> primes_v;

    for (int number=2; number<m_max; number++)
    {
        if(true == checkPrime(number))
        {
            primes_v.push_back(number);
        }
        else if (number%2 == 1)  // odd composite
        {
            if (false == validateGoldbachOtherConjecture(number, primes_v))
            {
               return number;
            }
        }
    }
    return 0;
}

int main()
{
    PE0046 pe0046;

    cout << pe0046.findSmallestOddComposite() << " is the smallest odd composite ";
    cout << "that cannot be written as the sum of a prime and twice a square."<<endl;

    return 0;
}