Given a positive integer N, check if it is Quartan prime or not. Print ‘Yes’ if it is a Quartan prime otherwise Print ‘No’.
Quartan Prime : A prime number of the form x4 + y4 where x > 0, y > 0, and x and y are integers is a Quartan Prime.
Quartan Prime in the range 1 – 100 are:
2, 17, 97
Examples:
Input : 17 Output : Yes Explanation : 17 is a prime number and can be expressed in the form of: x4 + y4 as ( 14 + 24 ) Input : 31 Output : No Explanation: 31 is prime number but can not be expressed in the form of x4 + y4.
A Simple Solution is to check if the given number is prime or not and then check if it can be expressed in the form of x4 + y4 or not.
An Efficient Solution is based on the fact that every Quartan Prime can also be expressed in the form 16*n + 1. So, we can check if a number is prime or not and can be expressed in the form of 16*n + 1 or not. If yes, Then the number is Quartan Prime otherwise not.
Below is the implementation of the above approach
C++
// CPP program to check if a number is// Quartan Prime or not#include <bits/stdc++.h>using namespace std;// 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;}// Driver Programint main(){ int n = 17; // Check if number is prime // and of the form 16*n + 1 if (isPrime(n) && (n % 16 == 1)) { cout << "YES"; } else { cout << "NO"; } return 0;} |
Java
// JAVA program to check if a number is// Quartan Prime or notclass GFG { // Function to check if a number // is prime or not static boolean 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; } // Driver Program public static void main(String[] args) { int n = 17; // Check if number is prime // and of the form 16*n + 1 if (isPrime(n) && (n % 16 == 1)) { System.out.println("YES"); } else { System.out.println("NO"); } }} |
Python3
# Python 3 program to check if a number is # Quartan Prime or not# Utility function to check# if a number is prime or notdef 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 i = 5 while(i * i <= n) : if (n % i == 0 or n % (i + 2) == 0) : return False i = i + 6 return True # Driver Code n = 17 # Check if number is prime # and of the form 16 * n + 1if(isPrime(n) and (n % 16 == 1) ): print("YES")else: print("NO") |
C#
// C# program to check if a number // is Quartan Prime or notusing System;class GFG {// Function to check if a number // is prime or notstatic bool 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;}// Driver Codepublic static void Main(){ int n = 17; // Check if number is prime // and of the form 16*n + 1 if (isPrime(n) && (n % 16 == 1)) { Console.WriteLine("YES"); } else { Console.WriteLine("NO"); }}}// This code is contributed// by inder_verma |
PHP
<?php// PHP program to check if a number // is Quartan Prime or not// 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;}// Driver Code$n = 17;// Check if number is prime// and of the form 16*n + 1if (isPrime($n) && ($n % 16 == 1)) { echo "YES";}else{ echo "NO";}// This code is contributed// anuj_67?> |
Javascript
<script>// Javascript program to check if a number is// Quartan Prime or not// 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 (var i = 5; i * i <= n; i = i + 6) { if (n % i == 0 || n % (i + 2) == 0) { return false; } } return true;}// Driver Programvar n = 17;// Check if number is prime// and of the form 16*n + 1if (isPrime(n) && (n % 16 == 1)) { document.write( "YES");}else { document.write( "NO");}// This code is contributed by itsok.</script> |
Output:
YES
Time Complexity: O(sqrt(n))
Auxiliary Space: O(1)
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