#include #include namespace prime { using us = unsigned short; using ui = unsigned int; using ull = unsigned long long; constexpr bool is_prime( const ull num ) noexcept; constexpr bool is_germain_prime( const ull ) noexcept; constexpr bool is_circular_prime( const ull ) noexcept; constexpr bool is_pandigital_prime( const ull ) noexcept; constexpr bool is_truncatable_prime( const ull ) noexcept; constexpr ull largest_prime_factor_of( const ull ); constexpr ull nth_prime( const ull ); constexpr ull sum_of_primes_below( const ull ) noexcept; } // namespace prime int main( int argc, char** argv ) { using namespace prime; std::cout << std::boolalpha; std::cout << "prime::is_prime() - Test\n"; std::cout << "1 -> " << is_prime( 1 ) << '\n'; std::cout << "2 -> " << is_prime( 2 ) << '\n'; std::cout << "71 -> " << is_prime( 71 ) << '\n'; std::cout << "\nprime::is_germain_prime() - Test\n"; std::cout << "5 -> " << is_germain_prime( 5 ) << '\n'; std::cout << "7 -> " << is_germain_prime( 7 ) << '\n'; std::cout << "35 -> " << is_germain_prime( 35 ) << '\n'; std::cout << "\nprime::is_circular_prime() - Test\n"; std::cout << "11 -> " << is_circular_prime( 11 ) << '\n'; std::cout << "100 -> " << is_circular_prime( 100 ) << '\n'; std::cout << "197 -> " << is_circular_prime( 197 ) << '\n'; std::cout << "\nprime::is_pandigital_prime() - Test\n"; std::cout << "13 -> " << is_pandigital_prime( 13 ) << '\n'; std::cout << "123 -> " << is_pandigital_prime( 123 ) << '\n'; std::cout << "2143 -> " << is_pandigital_prime( 2143 ) << '\n'; std::cout << "\nprime::is_truncatable_prime() - Test\n"; std::cout << "23 -> " << is_truncatable_prime( 23 ) << '\n'; std::cout << "101 -> " << is_truncatable_prime( 101 ) << '\n'; std::cout << "3797 -> " << is_truncatable_prime( 3797 ) << '\n'; std::cout << "\nprime::largest_prime_factor_of() - Test\n"; std::cout << "100 -> " << largest_prime_factor_of( 100 ) << '\n'; std::cout << "199 -> " << largest_prime_factor_of( 199 ) << '\n'; std::cout << "13195 -> " << largest_prime_factor_of( 13195 ) << '\n'; std::cout << "\nprime::nth_prime() - Test\n"; std::cout << "1 -> " << nth_prime( 1 ) << '\n'; std::cout << "5 -> " << nth_prime( 5 ) << '\n'; std::cout << "10 -> " << nth_prime( 10 ) << '\n'; std::cout << "\nprime::sum_of_primes_below() - Test\n"; std::cout << "2 -> " << sum_of_primes_below( 2 ) << '\n'; std::cout << "20 -> " << sum_of_primes_below( 20 ) << '\n'; std::cout << "100 -> " << sum_of_primes_below( 100 ) << '\n'; return EXIT_SUCCESS; } namespace prime { namespace { constexpr ull power( const ull num, const ui i ) { return ( i > 0 ? num * power( num, i - 1 ) : 1 ); } constexpr ull digits_of( const ull num ) { return ( num > 9 ? 1 + digits_of( num / 10 ) : 1 ); } constexpr bool is_prime_impl( const ull num, const ui i = 2 ) { return ( i <= num / 2 ? ( num % i ? is_prime_impl(num, i + 1) : false ) : true ); } constexpr ull shift_number( const ull num ) { if ( digits_of( num ) > 1) { return ( num / 10 + num % 10 * power( 10, digits_of( num - 1 ) ) ); } return num; } constexpr bool is_circular_prime_impl ( const ull num, const ull digits ) { return ( digits > 0 ? ( is_prime( num ) ? is_circular_prime_impl( shift_number( num ), digits - 1 ) : false ) : true ); } constexpr bool has_different_digits( const ull num ) { return ( num > 0 ? num % 10 != has_different_digits( num / 10 ) : 0 ); } constexpr bool contains_1_to_n( const ull num, const ui digits ) { return ( num > 0 ? ( num % 10 > digits ? false : contains_1_to_n( num / 10, digits ) ) : true ); } constexpr bool is_pandigital( const ull num ) { return ( has_different_digits( num ) && contains_1_to_n( num, digits_of( num ) ) ); } constexpr bool truncate_right( const ull num ) { return ( num > 0 ? ( is_prime( num ) ? truncate_right( num / 10 ) : false ) : true ); } constexpr bool truncate_left( const ull num ) { ull first_digit{ num / power( 10, digits_of( num ) - 1) }; return ( num > 0 ? ( is_prime( num ) ? truncate_left( num - ( first_digit * power( 10, digits_of( num ) - 1) ) ) : false ) : true ); } constexpr ull find_divisor( const ull num, const ull i = 2 ) { return ( num % i ? ( find_divisor( num, i + 1 ) ) : i ); } constexpr ull iterate_numbers( ull max, ull current_number = 3 ) { return ( is_prime( current_number ) ? ( max > 2 ? ( iterate_numbers( max - 1, current_number + 2 ) ) : current_number ) : iterate_numbers( max, current_number + 2 ) ); } constexpr ull sum_primes( ull max, ull current_number = 3) { return ( current_number < max ? ( is_prime( current_number ) ? current_number + sum_primes( max, current_number + 2 ) : sum_primes( max, current_number + 2 ) ) : 2 ); } } // namespace constexpr bool is_prime( const ull num ) noexcept { if ( num < 2 ) { return false; } return ( is_prime_impl( num ) ); } constexpr bool is_germain_prime( const ull num ) noexcept { return ( is_prime( num ) && is_prime( 2 * num + 1 ) ); } constexpr bool is_circular_prime( const ull num ) noexcept { return ( is_circular_prime_impl( num, digits_of( num ) - 1 ) ); } constexpr bool is_pandigital_prime( const ull num ) noexcept { return ( is_pandigital( num ) && is_prime( num ) ); } constexpr bool is_truncatable_prime( const ull num ) noexcept { return ( truncate_left( num ) && truncate_right( num / 10 ) ); } constexpr ull largest_prime_factor_of( const ull num ) { if ( num < 2 ) { throw std::invalid_argument( "No prime factor found." ); } return ( is_prime( num ) ? num : ( largest_prime_factor_of( num / find_divisor( num ) ) ) ); } constexpr ull nth_prime( const ull num ) { if ( !num ) { throw std::invalid_argument( "No prime number with index 0." ); } if ( num == 1 ) { return 2; } return ( iterate_numbers( num ) ); } constexpr ull sum_of_primes_below( const ull num ) noexcept { if ( num < 3 ) { return 0; } return ( sum_primes( num ) ); } } // namespace prime

Prime Library