#include <cmath>
#include <cstdint>
#include <iomanip>
#include <iostream>
#include <stdexcept>
#include <vector>

std::vector<bool> primes;

void initialise_primes(const int32_t& limit) {
	primes.resize(limit);
	for ( int32_t i = 2; i < limit; ++i ) {
		primes[i] = true;
	}

	for ( int32_t n = 2; n < sqrt(limit); ++n ) {
		for ( int32_t k = n * n; k < limit; k += n ) {
			primes[k] = false;
		}
	}
}

int32_t goldbach_function(const int32_t& number) {
	if (  number <= 2 || number % 2 == 1 ) {
		throw std::invalid_argument("Argument must be even and greater than 2: " + std::to_string(number));
	}

	int32_t result = 0;
	for ( int32_t i = 1; i <= number / 2; ++i ) {
		if ( primes[i] && primes[number - i] ) {
			result++;
		}
	}
	return result;
}

int main() {
	initialise_primes(2'000'000);

	std::cout << "The first 100 Goldbach numbers:" << std::endl;
	for ( int32_t n = 2; n < 102; ++n ) {
		std::cout << std::setw(3) << goldbach_function(2 * n) << ( n % 10 == 1 ? "\n" : "" );
	}

	std::cout << "\n" << "The 1,000,000th Goldbach number = " << goldbach_function(1'000'000) << std::endl;
}