Task: Wieferich primes


C++: #include <cstdint>
#include <iostream>
#include <vector>

std::vector<bool> prime_sieve(uint64_t limit) {
    std::vector<bool> sieve(limit, true);
    if (limit > 0)
        sieve[0] = false;
    if (limit > 1)
        sieve[1] = false;
    for (uint64_t i = 4; i < limit; i += 2)
        sieve[i] = false;
    for (uint64_t p = 3; ; p += 2) {
        uint64_t q = p * p;
        if (q >= limit)
            break;
        if (sieve[p]) {
            uint64_t inc = 2 * p;
            for (; q < limit; q += inc)
                sieve[q] = false;
        }
    }
    return sieve;
}

uint64_t modpow(uint64_t base, uint64_t exp, uint64_t mod) {
    if (mod == 1)
        return 0;
    uint64_t result = 1;
    base %= mod;
    for (; exp > 0; exp >>= 1) {
        if ((exp & 1) == 1)
            result = (result * base) % mod;
        base = (base * base) % mod;
    }
    return result;
}

std::vector<uint64_t> wieferich_primes(uint64_t limit) {
    std::vector<uint64_t> result;
    std::vector<bool> sieve(prime_sieve(limit));
    for (uint64_t p = 2; p < limit; ++p)
        if (sieve[p] && modpow(2, p - 1, p * p) == 1)
            result.push_back(p);
    return result;
}

int main() {
    const uint64_t limit = 5000;
    std::cout << "Wieferich primes less than " << limit << ":\n";
    for (uint64_t p : wieferich_primes(limit))
        std::cout << p << '\n';
}


C#: using System;
using System.Collections.Generic;
using System.Linq;

namespace WieferichPrimes {
    class Program {
        static long ModPow(long @base, long exp, long mod) {
            if (mod == 1) {
                return 0;
            }

            long result = 1;
            @base %= mod;
            for (; exp > 0; exp >>= 1) {
                if ((exp & 1) == 1) {
                    result = (result * @base) % mod;
                }
                @base = (@base * @base) % mod;
            }
            return result;
        }

        static bool[] PrimeSieve(int limit) {
            bool[] sieve = Enumerable.Repeat(true, limit).ToArray();

            if (limit > 0) {
                sieve[0] = false;
            }
            if (limit > 1) {
                sieve[1] = false;
            }

            for (int i = 4; i < limit; i += 2) {
                sieve[i] = false;
            }

            for (int p = 3; ; p += 2) {
                int q = p * p;
                if (q >= limit) {
                    break;
                }
                if (sieve[p]) {
                    int inc = 2 * p;
                    for (; q < limit; q += inc) {
                        sieve[q] = false;
                    }
                }
            }

            return sieve;
        }

        static List<int> WiefreichPrimes(int limit) {
            bool[] sieve = PrimeSieve(limit);
            List<int> result = new List<int>();
            for (int p = 2; p < limit; p++) {
                if (sieve[p] && ModPow(2, p - 1, p * p) == 1) {
                    result.Add(p);
                }
            }
            return result;
        }

        static void Main() {
            const int limit = 5000;
            Console.WriteLine("Wieferich primes less that {0}:", limit);
            foreach (int p in WiefreichPrimes(limit)) {
                Console.WriteLine(p);
            }
        }
    }
}