using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace NODER
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine("Please enter a number");
            long num = long.Parse(Console.ReadLine());
            while (num > 0)
            {
                if (perfectNum(num)== true) // Perfect Number
                {
                    Console.WriteLine("The number " + num + " is a perfect number");
                }
                else
                {
                    Console.WriteLine("The number " + num + " is not a perfect number");
                }
                if (Rising(num) == true) // Rising
                {
                    Console.WriteLine(num + " is a Rising number");
                }
                else
                {
                    Console.WriteLine(num + " is not a Rising number");
                }
                if (ReallyRising(num) == true) // Rising
                {
                    Console.WriteLine(num + " is a Really Rising number");
                }
                else
                {
                    Console.WriteLine(num + " is not a Really Rising number");
                }
                if (Descending(num) == true) // Rising
                {
                    Console.WriteLine(num + " is a Descending number");
                }
                else
                {
                    Console.WriteLine(num + " is not a Descending number");
                }
                if (ReallyDescending(num) == true) // Rising
                {
                    Console.WriteLine(num + " is a Really Descending number");
                }
                else
                {
                    Console.WriteLine(num + " is not a Really Descending number");
                }
                if (Palindrome(num) == true) // Palindrome
                {
                    Console.WriteLine(num + " is a Palindrome number");
                }
                else
                {
                    Console.WriteLine(num + " is not a Palindrome number");
                }
                if (Mersenne(num) == true) //Mersenne
                {
                    Console.WriteLine(num + " is a Mersenne number");
                }
                else
                {
                    Console.WriteLine(num + " is not a Mersenne Prime number");
                }
                if (Prime(num) == true)
                {
                    Console.WriteLine(num + " is a Prime number");
                    if (GPrime(num) == true) // Germain Prime
                    {
                        Console.WriteLine(num + " is a Germain Prime number");
                    }
                    else
                    {
                        Console.WriteLine(num + " is not a Germain Prime number");
                    }
                    if (FirstTwinPrime(num) == true)
                    {
                        Console.WriteLine(num + " is a Fist Twin Prime number");
                    }
                    else
                    {
                        Console.WriteLine(num + " is not a Fist Twin Prime number");
                    }
                    if (SecondTwinPrime(num) == true)
                    {
                        Console.WriteLine(num + " is a Second Twin Prime number");
                    }
                    else
                    {
                        Console.WriteLine(num + " is not a Second Twin Prime number");
                    }
                    if (Mersenne(num) == true)
                    {
                        Console.WriteLine(num + " is a Prime and a Mersenne number");
                    }
                    else
                    {
                        Console.WriteLine(num + " is not a Prime and a Mersenne number");
                    }
                }
                else
                {
                    Console.WriteLine(num + " is not a Prime numeber");
                    Console.WriteLine("--------------------------------------------");
                }
                Console.WriteLine("Please enter a number");
                num = long.Parse(Console.ReadLine());
            }
        }
        public static bool perfectNum(long num)
        {
            Console.WriteLine("-----------------Perfect ?---------------------");
            long sum = 1;
            Console.Write("1");
            for (long i = 2; i < num; i++)
            {
                if (num % i == 0)
                {
                    Console.Write("+" + i);
                    sum = sum + i;
                }
            }
            if (sum == num)
            {
                Console.Write("=" + num);
                Console.WriteLine("");
                return true;
            }
            else
            {
                Console.Write("!=" + num);
                Console.WriteLine("");
                return false;
            }
        }
        public static bool Rising(long num)
        {
            Console.WriteLine("-----------------Rising & Descending---------------------");
            if (num < 10)
            {
                return false;
            }
            long digits = getDigits(num);
            long last = num % 10;
            num = num / 10;
            long counter = 1;
            while (num > 0)
            {
                if (num % 10 <= last)
                {
                    counter++;
                }
                last = num % 10;
                num = num / 10;
            }
            if (counter == digits)
            {
                return true;
            }
            return false;
        }
        public static bool ReallyRising(long num)
        {
            if (num < 10)
            {
                return false;
            }
            long digits = getDigits(num);
            long last = num % 10;
            num = num / 10;
            long counter = 1;
            while (num > 0)
            {
                if (num % 10 < last)
                {
                    counter++;
                }
                last = num % 10;
                num = num / 10;
            }
            if (counter == digits)
            {
                return true;
            }
            return false;
        }
        public static bool Descending(long num)
        {
            if (num < 10)
            {
                return false;
            }
            long digits = getDigits(num);
            long last = num % 10;
            num = num / 10;
            long counter = 1;
            while (num > 0)
            {
                if (num % 10 >= last)
                {
                    counter++;
                }
                last = num % 10;
                num = num / 10;
            }
            if (counter == digits)
            {
                return true;
            }
            return false;
        }
        public static bool ReallyDescending(long num)
        {
            if (num < 10)
            {
                return false;
            }
            long digits = getDigits(num);
            long last = num % 10;
            num = num / 10;
            long counter = 1;
            while (num > 0)
            {
                if (num % 10 > last)
                {
                    counter++;
                }
                last = num % 10;
                num = num / 10;
            }
            if (counter == digits)
            {
                return true;
            }
            return false;
        }
        public static bool Palindrome(long num)
        {
            Console.WriteLine("-----------------Palindrome ?---------------------");
            long temp = num; // for defining num to its back after doing actions with num
            long digits = getDigits(num);
            long last;
            long rev = 0;
            long pow = 1;
            for (long i = 1; i <= (digits - 1); i++)
            {
                pow = pow * 10;
            }
            while (num > 0)
            {
                last = num % 10;
                rev = rev + (last * pow);
                num = num / 10;
                pow = pow / 10;
            }
            num = temp;
            Console.WriteLine("The input number is " + num);
            Console.WriteLine("Its reverse " + rev);
            if (num == rev)
            {
                return true;
            }
            else
            {
                return false;
            }
        }
        public static bool Mersenne(long num)
        {
            Console.WriteLine("-----------------Mersenne ?---------------------");
            long digits = getDigits(num);
            long pow = 1;
            for (long i = 1; i <= num; i++)
            {
                if ((2 * pow) - 1 == num)
                {
                    return true;
                }
                pow++;
            }
            return false;
        }
        public static bool Prime(long num)
        {
            Console.WriteLine("-----------------Prime ?---------------------");
            for (long i = 2; i <= num - 1; i++)
            {
                if (num % i == 0)
                {
                    return false;
                }
            }
            return true;
        }
        public static bool GPrime(long num)
        {
            Console.WriteLine("-----------------GPrime ?---------------------");
            for (long i = 2; i <= (((num * 2) + 1) - 1); i++)
            {
                if (((num * 2) + 1) % i == 0)
                {
                    return false;
                }
            }
            return true;
        }
        public static bool FirstTwinPrime(long num)
        {
            Console.WriteLine("-----------------FirstTwinPrime ?---------------------");
            for (long i = 2; i <= (num + 2) - 1; i++)
            {
                if ((num + 2) % i == 0)
                {
                    return false;
                }
            }
            return true;
        }
        public static bool SecondTwinPrime(long num)
        {
            Console.WriteLine("-----------------SecondTwinPrime ?---------------------");
                for (long i = 2; i <= (num - 2) - 1; i++)
                {
                    if ((num - 2) % i == 0)
                    {
                        return false;
                    }
                }
            return true;
        }
        public static long getDigits(long num)
        {
            long digits = 0;
            while (num > 0)
            {
                if ((num / 10) >= 0)
                {
                    digits++;
                }
                num = num / 10;
            }
            return digits;
        }
    }
}