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Check if a number is a Pythagorean Prime or not
  • Last Updated : 07 May, 2021

Given a positive integer N, check if it is Pythagorean prime or not. If it is a Pythagorean prime, print ‘Yes’ otherwise print ‘No’.
Pythagorean primes : A prime number of the form 4*n + 1 is a Pythagorean prime. It can also be expressed as sum of two squares. 
Pythagorean primes in the range 1 – 100 are: 
 

5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97 
 

Examples
 

Input : N = 5
Output : Yes
Explanation : 5 is a prime number and can be expressed 
in the form ( 4*n + 1 ) as ( 4*1 + 1 ).

Input : N = 13
Output : Yes
Explanation: 13 is a prime number and can be expressed 
in the form ( 4*n + 1 ) as ( 4*3 + 1 ).

 

A Simple Solution is to check first if the given number is prime or not and can be written in the form of 4*n + 1 or not. If yes, Then the number is Pythagorean prime, otherwise not.
Below is the implementation of the above approach
 

C++




// CPP program to check  if a number is
// Pythagorean 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 = 13;
     
    // Check if number is prime
    // and of the form 4*n+1
    if (isPrime(n) && (n % 4 == 1)) {
        cout << "YES";
    }
    else {
        cout << "NO";
    }
 
    return 0;
}

Java




// JAVA program to check  if a number is
// Pythagorean 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 = 13;
 
        // Check if number is prime
        // and of the form 4n+1
        if (isPrime(n) && (n % 4 == 1)) {
            System.out.println("YES");
        }
        else {
            System.out.println("NO");
        }
    }
}

Python3




# Python 3 program to check if a number is
# Pythagorean 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 = 13
     
# Check if number is prime
# and of the form 4n + 1
 
if(isPrime(n) and (n % 4 == 1)):
 
    print("YES")
 
else:
 
    print("NO")
      

C#




// C# program to check if a number
// is Pythagorean 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(string[] args)
{
    int n = 13;
 
    // Check if number is prime
    // and of the form 4n+1
    if (isPrime(n) && (n % 4 == 1))
    {
        Console.WriteLine("YES");
    }
    else
    {
        Console.WriteLine("NO");
    }
}
}
 
// This code is contributed by Shrikant13

PHP




<?php
// PHP program to check if
// a number is Pythagorean
// 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 or $n % 3 == 0)
        return false;
 
    for ($i = 5; $i * $i <= $n;
                 $i = $i + 6)
    {
        if ($n % $i == 0 or
            $n % ($i + 2) == 0)
        {
            return false;
        }
    }
     
    return true;
}
 
// Driver Code
$n = 13;
 
// Check if number is prime
// and of the form 4*n+1
if (isPrime($n) && ($n % 4 == 1))
{
    echo "YES";
}
else
{
    echo "NO";
}
 
// This code is contributed
// by inder_verma
?>

Javascript




<script>
 
 
// Javascript program to check  if a number is
// Pythagorean 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 = 13;
  
// Check if number is prime
// and of the form 4*n+1
if (isPrime(n) && (n % 4 == 1)) {
    document.write( "YES");
}
else {
    document.write( "NO");
}
 
// This code is contributed by itsok.
</script>
Output: 
YES

 

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