Comprobar si la diferencia de áreas de dos cuadrados es primo

Dados dos cuadrados con longitudes de lado  y  (a > b). La tarea es verificar si la diferencia de sus áreas es prima o no. Aquí la longitud del lado podría ser grande (1 < b < a < 10 ¹² ).
Ejemplos : 
 

Input : a = 6, b = 5
Output : Yes

Input : a = 61690850361, b = 24777622630    
Output : No

Aproximación: Dado que los lados son  y  . Por lo tanto, diferencia de sus áreas = (a ² – b ² ), que se puede expresar como (a – b)(a + b) . Esto es primo si y solo si a – b = 1 y a + b es un primo . Como a+b es como mucho 2×10 ¹² , podemos usar la división de prueba para verificar su primalidad.
A continuación se muestra la implementación de la idea anterior: 
 

// C++ program to check if difference of
// areas of two squares is prime or not
// when side length is large
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to check if number is prime
bool isPrime(long long 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 (long long int i = 5; i * i <= n; i = i + 6)
        if (n % i == 0 || n % (i + 2) == 0)
            return false;
 
    return true;
}
 
// Function to check if difference of areas of
// square is prime
bool isDiffPrime(long long int a, long long int b)
{
    // when a+b is prime and a-b is 1
    if (isPrime(a + b) && a - b == 1)
        return true;
    else
        return false;
}
 
// Driver code
int main()
{
    long long int a = 6, b = 5;
 
    if (isDiffPrime(a, b))
        cout << "Yes";
    else
        cout << "No";
 
    return 0;
}

// Java program to check if difference
// of areas of two squares is prime or
// not when side length is large
class GFG
{
     
// Function to check if number
// is prime
static boolean isPrime(long 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 (long i = 5; i * i <= n; i = i + 6)
        if (n % i == 0 || n % (i + 2) == 0)
            return false;
 
    return true;
}
 
// Function to check if difference
// of areas of square is prime
static boolean isDiffPrime(long a, long b)
{
    // when a+b is prime and a-b is 1
    if (isPrime(a + b) && a - b == 1)
        return true;
    else
        return false;
}
 
// Driver code
public static void main(String []args)
{
    long a = 6, b = 5;
 
    if (isDiffPrime(a, b))
        System.out.println("Yes");
    else
        System.out.println("No");
}
}
 
// This code is contributed by ihritik

// C# program to check if difference
// of areas of two squares is prime
// or not when side length is large
using System;
 
class GFG
{
// Function to check if number
// is prime
static bool isPrime(long 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 (long i = 5;
              i * i <= n; i = i + 6)
        if (n % i == 0 || n % (i + 2) == 0)
            return false;
 
    return true;
}
 
// Function to check if difference
// of areas of square is prime
static bool isDiffPrime(long a, long b)
{
    // when a+b is prime and a-b is 1
    if (isPrime(a + b) && a - b == 1)
        return true;
    else
        return false;
}
 
// Driver code
public static void Main()
{
    long a = 6, b = 5;
 
    if (isDiffPrime(a, b))
        Console.WriteLine("Yes");
    else
        Console.WriteLine("No");
}
}
 
// This code is contributed by ihritik

# Python3 program to check if
# difference of areas of two
# squares is prime or not when
# side length is large
 
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
 
# Function to check if difference
# of areas of square is prime
def isDiffPrime(a, b):
 
    # when a+b is prime and a-b is 1
    if (isPrime(a + b) and a - b == 1):
        return True
    else:
        return False
 
# Driver code
a = 6
b = 5
 
if (isDiffPrime(a, b)):
    print("Yes")
else:
    print("No")
 
# This code is contributed by ihritik

<?php
// PHP program to check if difference
// of areas of two squares is prime
// or not when side length is large
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;
}
 
// Function to check if difference
// of areas of square is prime
function isDiffPrime($a, $b)
{
    # when a+b is prime and a-b is 1
    if (isPrime($a + $b) &&
                $a - $b == 1)
        return true;
    else
        return false;
 
}
 
// Driver code
$a = 6;
$b = 5;
 
if (isDiffPrime($a, $b))
    echo "Yes";
else
    echo "No";
 
// This code is contributed by ihritik
?>

<script>
// Javascript program to check if difference
// of areas of two squares is prime
// or not when side length is large
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(let i = 5; i * i <= n;
                i = i + 6)
        if (n % i == 0 ||
            n % (i + 2) == 0)
        return false;
 
    return true;
}
 
// Function to check if difference
// of areas of square is prime
function isDiffPrime(a, b)
{
    // when a+b is prime and a-b is 1
    if (isPrime(a + b) &&
                a - b == 1)
        return true;
    else
        return false;
 
}
 
// Driver code
let a = 6;
let b = 5;
 
if (isDiffPrime(a, b))
    document.write("Yes");
else
    document.write("No");
 
// This code is contributed by Saurabh Jaiswal
</script>

Yes