The following C++ code implements the Genuine Sieve of Eratosthenes algorithm as described in Melissa O'Neill's classic paper.  On my MacBook it computes the first 1,000,000 primes in about 11 seconds.$ ./a.out | head -1000000 | tail -115485863$Just looking for general code review comments here. At least two parts of sieverator smell really bad to me, but I'm not sure of the proper way to fix them while still preserving the general STLishness of this code. For example, I really want to keep using the ranged for-loop in main.#include <cassert>#include <functional>#include <iostream>#include <memory>#include <queue>#include <utility>template<typename Int>class iotarator {    Int value = 0;    Int step = 1;public:    explicit iotarator() = default;    explicit iotarator(Int v) : value(v) {}    explicit iotarator(Int v, Int s) : value(v), step(s) {}    Int operator*() const { return value; }    iotarator& operator++() { value += step; return *this; }    iotarator operator++(int) { auto ret = *this; ++*this; return ret; }    bool operator==(const iotarator& rhs) const {        return value == rhs.value && step == rhs.step;    }    bool operator!=(const iotarator& rhs) const { return !(*this == rhs); }};template<class Int>class sieverator {    struct erased_iterator {        virtual Int dereference() = 0;        virtual void increment() = 0;    };    template<class It>    class derived_iterator : public erased_iterator {        It it;    public:        derived_iterator(It it) : it(std::move(it)) {}        Int dereference() override { return *it; }        void increment() override { ++it; }    };    Int m_current;    std::unique_ptr<erased_iterator> m_ptr;    explicit sieverator() {}  // used by .end()public:    template<class It>    explicit sieverator(It it) :        m_current(*it),        m_ptr(std::make_unique<derived_iterator<It>>(std::move(it)))    {}    sieverator begin() { return std::move(*this); }    sieverator end() const { return sieverator{}; }    bool operator==(const sieverator&) const { return false; }    bool operator!=(const sieverator&) const { return true; }    Int operator*() const {        return m_current;    }    sieverator& operator++() {        cross_off_multiples_of_prime(m_current);        do {            m_ptr->increment();            m_current = m_ptr->dereference();        } while (is_already_crossed_off(m_current));        return *this;    }    sieverator& operator++(int) = delete;private:    struct pair {        Int next_crossed_off_value;        Int prime_increment;        explicit pair(Int a, Int b) : next_crossed_off_value(a), prime_increment(b) {}        bool operator<(const pair& rhs) const {            return next_crossed_off_value < rhs.next_crossed_off_value ? true                 : next_crossed_off_value > rhs.next_crossed_off_value ? false                 : prime_increment < rhs.prime_increment;        }        bool operator>(const pair& rhs) const { return rhs < *this; }    };    template<class T> using min_heap = std::priority_queue<T, std::vector<T>, std::greater<>>;    min_heap<pair> m_pq;    bool is_already_crossed_off(Int value) {        if (value != m_pq.top().next_crossed_off_value) {            return false;        } else {            do {                auto x = m_pq.top();                m_pq.pop();                m_pq.emplace(x.next_crossed_off_value + x.prime_increment, x.prime_increment);            } while (value == m_pq.top().next_crossed_off_value);            return true;        }    }    void cross_off_multiples_of_prime(Int value) {        m_pq.emplace(value * value, value);    }};int main(){    iotarator<__int128_t> iota(2);    sieverator<__int128_t> sieve(iota);    for (int p : sieve) {        std::cout << p << std::endl;    }}
The Genuine Sieve of Eratosthenes in C++14
c++;c++14;iterator;sieve of eratosthenes