Check if a number is a Pythagorean Prime or not
Last Updated :
20 Aug, 2022
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 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");
}
}
}
# 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# 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 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
?>
<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>
Time Complexity: O(sqrt(n))
Auxiliary Space: O(1)
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