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//Prime is King

//Rules
//ABC == Prime
//AB  == Prime
// BC == Prime

#include<iostream>
#include<bits/stdc++.h> //Vector - Stuff

//Globale Variables
std::vector<int> numbers = {};	//all Primes

//Functions
bool test_2_digits (int digits);

int main() {
	
	//Variables	
	std::vector<int> abc = {};
	bool b_abc = false;				//a Boolean for ABC
	bool b_ab  = false;				//a Boolean for AB
	bool b_bc  = false;				//a Boolean for  BC
	
	//Fill "numbers"
	for (int i = 2; i < 1000; i++) {
		numbers.push_back(i);
	} 
	
	//Filter "numbers" => find all Primes till 999
	for (int i = 0; i < numbers.size() - 1; i++) {
		for (int j = 0; j < numbers.size() - 1; j++) {
			if (numbers[j] % numbers[i] == 0 ^ numbers[i] == numbers[j]) {
				numbers.erase(numbers.begin() + j);				
			} 
		}
	
		//Test: Size of ABC == 3
		if (numbers[i] > 100) {
			b_abc = true;
		}
		
		//Test: AB is Prime
		if (b_abc) {
			b_ab = test_2_digits(numbers[i] / 10);	
		}
		
		//Test: BC is Prime
		if (b_ab) {
			b_bc = test_2_digits(numbers[i] % 100);
		}
		
		//Push in Vector
		if (b_bc) {
			abc.push_back(numbers[i]);
		}
		
		//Reset Booleans
		b_abc = false;
		b_ab  = false;
		b_bc  = false;				
	}	
	
	//Print the Primes
	std::cout << "Primes left: \n";
	for (int i = 0; i < abc.size(); i++) {
		std::cout << abc[i] << "\t";
	}
		
	return 0;
}

//Compare AB/BC with proved 2-Digit-Primes
bool test_2_digits (int digits) {
	int n = 0;
	while (numbers[n] < 100) {
		if (digits == numbers[n]) {
			return true;
		}
		n++;
	}	
	return false;
}