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
// 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 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" );
}
}
} |
# 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# 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 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 ?> |
<script> // Javascript 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 ( var i = 5; i * i <= n; i = i + 6) {
if (n % i == 0 || n % (i + 2) == 0) {
return false ;
}
}
return true ;
} // Driver Program var n = 17;
// Check if number is prime // and of the form 16*n + 1 if (isPrime(n) && (n % 16 == 1)) {
document.write( "YES" );
} else {
document.write( "NO" );
} // This code is contributed by itsok. </script> |
YES
Time Complexity: O(sqrt(n))
Auxiliary Space: O(1)