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Check if a number is Quartan Prime or not
  • Last Updated : 17 Jan, 2019

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 not
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 Program
int 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 not
  
class 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 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
    
    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 + 1
  
if(isPrime(n) and (n % 16 == 1) ):
  
    print("YES")
  
else:
  
    print("NO")
  
            

C#




// C# program to check if a number 
// is Quartan Prime or not
using System;
  
class GFG 
{
  
// Function to check if a number 
// is prime or not
static 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 Code
public 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 not
function 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 + 1
if (isPrime($n) && ($n % 16 == 1)) 
{
    echo "YES";
}
else 
{
    echo "NO";
}
  
// This code is contributed
// anuj_67
?>
Output:
YES

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