# Check if a number is a Pythagorean Prime or not

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 ).
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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

 ` `

Output:

```YES
```

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Improved By : shrikanth13, inderDuMCA