#include <iostream>
#include <deque>

template<typename T>
bool is_odd(T value)
{
    return value & 1;
}

std::deque<std::size_t> atkin(std::size_t max)
{
    std::deque<std::size_t> result{ 2, 3, 5 };
    std::deque<bool> sieve(max, false);

    for (std::size_t n{ 7 }; n < sieve.size(); ++n) {
        auto rem{ n % 60 };
        if (!is_odd(rem))
            continue;

        if (rem == 1 || rem == 13 || rem == 17 || rem == 29 || rem == 37 || rem == 41 || rem == 49 || rem == 53) {
            // 4x² + y² = n
            for (std::size_t y{ 0 }; y < n; ++y)
                for (std::size_t x{ 0 }; x < n; ++x)
                    if (4 * (x * x) + y * y == n)
                        sieve[n] = !sieve[n];
        }
        else if (rem == 7 || rem == 19 || rem == 31 || rem == 43) {
            // 3x² + y² = n
            for (std::size_t y{ 0 }; y < n; ++y)
                for (std::size_t x{ 0 }; x < n; ++x)
                    if (3 * (x * x) + y * y == n)
                        sieve[n] = !sieve[n];
        }
        else if (rem == 11 || rem == 23 || rem == 47 || rem == 59) {
            // 3x² − y² = n | x > y
            for (std::size_t y{ 0 }; y < n; ++y)
                for (std::size_t x{ y + 1 }; x < n; ++x)
                    if (3 * (x * x) - y * y == n)
                        sieve[n] = !sieve[n];
        }
    }

    for (std::size_t n{}; n < sieve.size(); ++n) {
        if (!sieve[n])
            continue;

        result.push_back(n);

        for (auto not_prime{ n * n }; not_prime <= max; not_prime += n)
            sieve[not_prime] = false;
    }

    return result;
}



int main(){
	std::cout << std::unitbuf;
	
    for(auto x : atkin(10000))
        std::cout << x << ' ';
}