Task: Pierpont primes


C++: #include <cassert>
#include <algorithm>
#include <iomanip>
#include <iostream>
#include <vector>
#include <gmpxx.h>

using big_int = mpz_class;

bool is_prime(const big_int& n) {
    return mpz_probab_prime_p(n.get_mpz_t(), 25);
}

template <typename integer>
class n_smooth_generator {
public:
    explicit n_smooth_generator(size_t n);
    integer next();
    size_t size() const {
        return results_.size();
    }
private:
    std::vector<size_t> primes_;
    std::vector<size_t> index_;
    std::vector<integer> results_;
    std::vector<integer> queue_;
};

template <typename integer>
n_smooth_generator<integer>::n_smooth_generator(size_t n) {
    for (size_t p = 2; p <= n; ++p) {
        if (is_prime(p)) {
            primes_.push_back(p);
            queue_.push_back(p);
        }
    }
    index_.assign(primes_.size(), 0);
    results_.push_back(1);
}

template <typename integer>
integer n_smooth_generator<integer>::next() {
    integer last = results_.back();
    for (size_t i = 0, n = primes_.size(); i < n; ++i) {
        if (queue_[i] == last)
            queue_[i] = results_[++index_[i]] * primes_[i];
    }
    results_.push_back(*min_element(queue_.begin(), queue_.end()));
    return last;
}

void print_vector(const std::vector<big_int>& numbers) {
    for (size_t i = 0, n = numbers.size(); i < n; ++i) {
        std::cout << std::setw(9) << numbers[i];
        if ((i + 1) % 10 == 0)
            std::cout << '\n';
    }
    std::cout << '\n';
}

int main() {
    const int max = 250;
    std::vector<big_int> first, second;
    int count1 = 0;
    int count2 = 0;
    n_smooth_generator<big_int> smooth_gen(3);
    big_int p1, p2;

    while (count1 < max || count2 < max) {
        big_int n = smooth_gen.next();
        if (count1 < max && is_prime(n + 1)) {
            p1 = n + 1;
            if (first.size() < 50)
                first.push_back(p1);
            ++count1;
        }
        if (count2 < max && is_prime(n - 1)) {
            p2 = n - 1;
            if (second.size() < 50)
                second.push_back(p2);
            ++count2;
        }
    }
    
    std::cout << "First 50 Pierpont primes of the first kind:\n";
    print_vector(first);
    std::cout << "First 50 Pierpont primes of the second kind:\n";
    print_vector(second);
    
    std::cout << "250th Pierpont prime of the first kind: " << p1 << '\n';
    std::cout << "250th Pierpont prime of the second kind: " << p2 << '\n';
    return 0;
}



Go: package main

import (
    "fmt"
    big "github.com/ncw/gmp"
    "sort"
)

var (
    one   = new(big.Int).SetUint64(1)
    two   = new(big.Int).SetUint64(2)
    three = new(big.Int).SetUint64(3)
)

func pierpont(ulim, vlim int, first bool) []*big.Int {
    p := new(big.Int)
    p2 := new(big.Int).Set(one)
    p3 := new(big.Int).Set(one)   
    var pp []*big.Int
    for v := 0; v < vlim; v++ {
        for u := 0; u < ulim; u++ {
            p.Mul(p2, p3)
            if first {
                p.Add(p, one)
            } else {
                p.Sub(p, one)
            }
            if p.ProbablyPrime(10) {
                q := new(big.Int)
                q.Set(p)
                pp = append(pp, q)
            }
            p2.Mul(p2, two)
        }
        p3.Mul(p3, three)
        p2.Set(one)
    }
    sort.Slice(pp, func(i, j int) bool {
        return pp[i].Cmp(pp[j]) < 0
    })
    return pp
}
func main() {
    fmt.Println("First 50 Pierpont primes of the first kind:")
    pp := pierpont(120, 80, true)
    for i := 0; i < 50; i++ {
        fmt.Printf("%8d ", pp[i])
        if (i-9)%10 == 0 {
            fmt.Println()
        }
    }
    fmt.Println("\nFirst 50 Pierpont primes of the second kind:")
    pp2 := pierpont(120, 80, false)
    for i := 0; i < 50; i++ {
        fmt.Printf("%8d ", pp2[i])
        if (i-9)%10 == 0 {
            fmt.Println()
        }
    }
    fmt.Println("\n250th Pierpont prime of the first kind:", pp[249])
    fmt.Println("\n250th Pierpont prime of the second kind:", pp2[249])
}