Given a positive integer N, the task is to check if N is a Factorial prime or not. If it is a factorial prime then print YES else print NO.
Note: In mathematics, a factorial prime number is a prime number that is one less than or one more than a factorial of any number. First few factorial primes are 2, 3, 5, 7, 23, 719, 5039, ….
Examples:
Input: N = 23
Output: YES
23 is a prime number and one less than factorial of 4 (4! = 24).
Input: 11
Output: NO
11 is a prime number but can not be expressed as either n! + 1 or n! – 1.
Approach: In order for N to be factorial number, N must be a prime and either N – 1 or N + 1 should be the value of factorial of any number.
- If N is not prime then print No.
- Else set fact = 1 and starting from i = 1 update fact = fact * i, if fact = N – 1 or fact = N + 1 then print Yes.
- Repeat the above step until fact ? N + 1 and if the condition is not satisfied then print No in the end.
Below is the implementation of the above approach:
C++
// C++ program to check if given// number is a factorial prime#include <bits/stdc++.h>using namespace std;// Utility function to check// if a number is prime or notbool isPrime(int n){ // Corner cases if (n <= 1) return false; if (n <= 3) return true; // This is checked so that we can skip // middle five numbers in below loop if (n % 2 == 0 || n % 3 == 0) return false; for (int i = 5; i * i <= n; i = i + 6) if (n % i == 0 || n % (i + 2) == 0) return false; return true;}// Function that returns true if n is a factorial primebool isFactorialPrime(long n){ // If n is not prime then return false if (!isPrime(n)) return false; long fact = 1; int i = 1; while (fact <= n + 1) { // Calculate factorial fact = fact * i; // If n is a factorial prime if (n + 1 == fact || n - 1 == fact) return true; i++; } // n is not a factorial prime return false;}// Driver codeint main(){ int n = 23; if (isFactorialPrime(n)) cout << "Yes"; else cout << "No"; return 0;} |
C
// C program to check if given// number is a factorial prime#include <stdio.h>#include<stdbool.h>// Utility function to check// if a number is prime or notbool isPrime(int n){ // corner cases if (n <= 1) return false; if (n <= 3) return true; // This is checked so that we can skip // middle five numbers in below loop if (n % 2 == 0 || n % 3 == 0) return false; for (int i = 5; i * i <= n; i = i + 6) if (n % i == 0 || n % (i + 2) == 0) return false; return true;}// Function that returns true if n is a factorial primebool isFactorialPrime(long n){ // If n is not prime then return false if (!isPrime(n)) return false; long fact = 1; int i = 1; while (fact <= n + 1) { // Calculate factorial fact = fact * i; // if n is a factorial prime if (n + 1 == fact || n - 1 == fact) return true; i++; } // n is not a factorial prime return false;}// Driver codeint main(){ int n = 23; if (isFactorialPrime(n)) printf("Yes"); else printf("No"); return 0;}// This code is contributed by allwink45. |
Java
// Java program to check if given// number is a factorial primeclass GFG { // Utility function to check // if a number is prime or not static boolean isPrime(long n) { // Corner cases if (n <= 1) return false; if (n <= 3) return true; // This is checked so that we can skip // middle five numbers in below loop if (n % 2 == 0 || n % 3 == 0) return false; for (int i = 5; i * i <= n; i = i + 6) if (n % i == 0 || n % (i + 2) == 0) return false; return true; } // Function that returns true if n is a factorial prime static boolean isFactorialPrime(long n) { // If n is not prime then return false if (!isPrime(n)) return false; long fact = 1; int i = 1; while (fact <= n + 1) { // Calculate factorial fact = fact * i; // If n is a factorial prime if (n + 1 == fact || n - 1 == fact) return true; i++; } // n is not a factorial prime return false; } // Driver code public static void main(String args[]) { int n = 23; if (isFactorialPrime(n)) System.out.println("Yes"); else System.out.println("No"); }} |
Python3
# Python3 program to check if given # number is a factorial prime # from math lib import sqrt functionfrom math import sqrt# Utility function to check # if a number is prime or not def isPrime(n) : # Corner cases if (n <= 1) : return False if (n <= 3) : return True # This is checked so that we can skip # middle five numbers in below loop if (n % 2 == 0 or n % 3 == 0) : return False for i in range(5, int(sqrt(n)) + 1, 6) : if (n % i == 0 or n % (i + 2) == 0) : return False return True# Function that returns true if n # is a factorial prime def isFactorialPrime(n) : # If n is not prime then return false if (not isPrime(n)) : return False fact = 1 i = 1 while (fact <= n + 1) : # Calculate factorial fact = fact * i # If n is a factorial prime if (n + 1 == fact or n - 1 == fact) : return True i += 1 # n is not a factorial prime return False# Driver code if __name__ == "__main__" : n = 23 if (isFactorialPrime(n)) : print("Yes") else : print("No")# This code is contributed by Ryuga |
C#
// C# program to check if given// number is a factorial primeusing System;class GFG { // Utility function to check // if a number is prime or not static bool isPrime(long n) { // Corner cases if (n <= 1) return false; if (n <= 3) return true; // This is checked so that we can skip // middle five numbers in below loop if (n % 2 == 0 || n % 3 == 0) return false; for (int i = 5; i * i <= n; i = i + 6) if (n % i == 0 || n % (i + 2) == 0) return false; return true; } // Function that returns true if n is a factorial prime static bool isFactorialPrime(long n) { // If n is not prime then return false if (!isPrime(n)) return false; long fact = 1; int i = 1; while (fact <= n + 1) { // Calculate factorial fact = fact * i; // If n is a factorial prime if (n + 1 == fact || n - 1 == fact) return true; i++; } // n is not a factorial prime return false; } // Driver code public static void Main() { int n = 23; if (isFactorialPrime(n)) Console.WriteLine("Yes"); else Console.WriteLine("No"); }} |
PHP
<?php // PHP program to check if given number // is a factorial prime// Utility function to check if a // number is prime or notfunction isPrime($n){ // Corner cases if ($n <= 1) return false; if ($n <= 3) return true; // This is checked so that we can skip // middle five numbers in below loop if ($n % 2 == 0 || $n % 3 == 0) return false; for ($i = 5; $i * $i <= $n; $i = $i + 6) if ($n % $i == 0 || $n % ($i + 2) == 0) return false; return true;}// Function that returns true if // n is a factorial primefunction isFactorialPrime($n){ // If n is not prime then return false if (!isPrime($n)) return false; $fact = 1; $i = 1; while ($fact <= $n + 1) { // Calculate factorial $fact = $fact * $i; // If n is a factorial prime if ($n + 1 == $fact || $n - 1 == $fact) return true; $i++; } // n is not a factorial prime return false;}// Driver code$n = 23;if (isFactorialPrime($n)) echo "Yes";else echo "No";// This code is contributed by ita_c?> |
Javascript
// Javascript program to check if given number// is a factorial prime// Utility function to check if a// number is prime or notfunction isPrime(n){ // Corner cases if (n <= 1) return false; if (n <= 3) return true; // This is checked so that we can skip // middle five numbers in below loop if (n % 2 == 0 || n % 3 == 0) return false; for (let i = 5; i * i <= n; i = i + 6) if (n % i == 0 || n % (i + 2) == 0) return false; return true;}// Function that returns true if// n is a factorial primefunction isFactorialPrime(n){ // If n is not prime then return false if (!isPrime(n)) return false; let fact = 1; let i = 1; while (fact <= n + 1) { // Calculate factorial fact = fact * i; // If n is a factorial prime if (n + 1 == fact || n - 1 == fact) return true; i++; } // n is not a factorial prime return false;}// Driver codelet n = 23;if (isFactorialPrime(n)) document.write("Yes");else document.write("No");// This code is contributed by gfgking |
Output:
Yes
Time Complexity: O(sqrtn)
Auxiliary Space: O(1)
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