Definitions

   A   safe prime   is a prime   p   and where   (p-1)/2   is also prime.
   The corresponding prime  (p-1)/2   is known as a   Sophie Germain   prime.
   An   unsafe prime   is a prime   p   and where   (p-1)/2   isn't   a prime.
   An   unsafe prime   is a prime that   isn't   a   safe   prime.


Task

   Find and display (on one line) the first   35   safe primes.
   Find and display the   count   of the safe primes below   1,000,000.
   Find and display the   count   of the safe primes below 10,000,000.
   Find and display (on one line) the first   40   unsafe primes.
   Find and display the   count   of the unsafe primes below   1,000,000.
   Find and display the   count   of the unsafe primes below 10,000,000.
   (Optional)   display the   counts   and   "below numbers"   with commas.
Show all output here.



Related Task

   strong and weak primes.


Also see

   The OEIS article:     safe   primes.
   The OEIS article:   unsafe primes.


#include <algorithm>
#include <iostream>
#include <iterator>
#include <locale>
#include <vector>
#include "prime_sieve.hpp"
 
const int limit1 = 1000000;
const int limit2 = 10000000;
 
class prime_info {
public:
    explicit prime_info(int max) : max_print(max) {}
    void add_prime(int prime);
    void print(std::ostream& os, const char* name) const;
private:
    int max_print;
    int count1 = 0;
    int count2 = 0;
    std::vector<int> primes;
};
 
void prime_info::add_prime(int prime) {
    ++count2;
    if (prime < limit1)
        ++count1;
    if (count2 <= max_print)
        primes.push_back(prime);
}
 
void prime_info::print(std::ostream& os, const char* name) const {
    os << "First " << max_print << " " << name << " primes: ";
    std::copy(primes.begin(), primes.end(), std::ostream_iterator<int>(os, " "));
    os << '\n';
    os << "Number of " << name << " primes below " << limit1 << ": " << count1 << '\n';
    os << "Number of " << name << " primes below " << limit2 << ": " << count2 << '\n';
}
 
int main() {
    // find the prime numbers up to limit2
    prime_sieve sieve(limit2);
 
    // write numbers with groups of digits separated according to the system default locale
    std::cout.imbue(std::locale(""));
 
    // count and print safe/unsafe prime numbers
    prime_info safe_primes(35);
    prime_info unsafe_primes(40);
    for (int p = 2; p < limit2; ++p) {
        if (sieve.is_prime(p)) {
            if (sieve.is_prime((p - 1)/2))
                safe_primes.add_prime(p);
            else
                unsafe_primes.add_prime(p);
        }
    }
    safe_primes.print(std::cout, "safe");
    unsafe_primes.print(std::cout, "unsafe");
    return 0;
}