质数的和与积

两个数的和是S,他们积最大是多少

输入 50 输出 589

#include
#include
#include
#include
#include
using namespace std;
bool Prime(vector a, int X)
{
	int x = sqrt(X);
	for (size_t i = 0; i < a.size(); ++i){
		if (X%a[i] == 0){
			return false;
		}
		else if (a[i]>x){
			break;
		}
	}
	return true;
}
int main()
{
	int N;
	cin >> N;
	vector a;
	a.push_back(2);
	a.push_back(3);
	for (int i = 4; i < N; ++i){
		if (Prime(a,i)){
			a.push_back(i);
		}
	}
	int Max = 0;
	set b(a.begin(), a.end());
	auto it = upper_bound(b.begin(), b.end(), N / 2);
	for (; it != b.begin();--it){
		auto it1 = b.find(N - *it);
		if (it1 != b.end()){
			if ((*it)*(N - *it)>Max){
				Max = (*it)*(N - *it);
			}
		}
	}
	if (it == b.begin() && ( b.find(N - *it)!=b.end())){
		if ((*it)*(N - *it)>Max){
			Max = (*it)*(N - *it);
		}
	}
	cout << Max << endl;
	system("pause");
	return 0;
}