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Check if N is a Balanced Prime number or not
• Last Updated : 18 Mar, 2021

Given a positive integer N, the task is to check if N is a Balanced Prime number or not.

In number theory, a Balanced Prime  is a prime number with equal-sized prime gaps above and below it, so that it is equal to the arithmetic mean of the nearest primes above and below. Or to put it algebraically, given a prime number p<sub>n</sub>, where n is its index in the ordered set of prime numbers, First  few balanced prime are 5, 53, 157, 173……

Examples:

Input: N = 5
Output: Yes
5 is 3rd prime number, the arithmetic mean of 2nd and 4th prime number i.e. 3 and 7 is 5.
so 5 is a Balanced prime.

Input: N = 11
Output: No

Approach:

• If N is not a prime number or it is the first prime number i.e. 2 then print No.
• Else find the primes closest to N (one on the left and one on the right) and store their arithmetic mean in mean.
• If N == mean then print Yes.
• Else print No.

Below is the implementation of the above approach:

## C++

 // C++ program to check if a// given number is Balanced prime#include using namespace std; // Utility function to check// if a number is prime or notbool 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;} // Function that returns true// if n is a Balanced primebool isBalancedPrime(int n){     // If n is not a prime number or    // n is the first prime then    // return false    if (!isPrime(n) || n == 2)        return false;     // Initialize previous_prime to    // n - 1 and next_prime to n + 1    int previous_prime = n - 1;    int next_prime = n + 1;     // Find next prime number    while (!isPrime(next_prime))        next_prime++;     // Find previous prime number    while (!isPrime(previous_prime))        previous_prime--;     // Arithmetic mean    int mean = (previous_prime +                next_prime) / 2;     // If n is a weak prime    if (n == mean)        return true;    else        return false;} // Driver codeint main(){    int n = 53;     if (isBalancedPrime(n))        cout << "Yes";    else        cout << "No";         return 0;} // This code is contributed by himanshu77

## Java

 // Java program to check if a// given number is Balanced primeclass GFG{     // Utility 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 += 6)        if (n % i == 0 ||            n % (i + 2) == 0)            return false;    return true;} // Function that returns true// if n is a Balanced prime    static boolean isBalancedPrime(int n){         // If n is not a prime number    // or n is the first prime    // then return false    if (!isPrime(n) || n == 2)        return false;     // Initialize previous_prime to    // n - 1 and next_prime to n + 1    int previous_prime = n - 1;    int next_prime = n + 1;     // Find next prime number    while (!isPrime(next_prime))        next_prime++;     // Find previous prime number    while (!isPrime(previous_prime))        previous_prime--;     // Arithmetic mean    int mean = (previous_prime +                next_prime) / 2;     // If n is a weak prime    if (n == mean)        return true;    else        return false;}     // Driver codepublic static void main(String[] args){    int n = 53;     if (isBalancedPrime(n))        System.out.println("Yes");    else        System.out.println("No");}} // This code is contributed by stutipathak31jan

## Python3

 # Python3 program to check if a# given number is Balanced prime # Utility function to check# if a number is prime or notdef 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 += 6             return True # Function that returns true# if n is a Balanced primedef isBalancedPrime(n):         # If n is not a prime number    # or n is the first prime    # then return false    if not isPrime(n) or n == 2:        return False         # Initialize previous_prime to     # n - 1 and next_prime to n + 1    previous_prime = n - 1    next_prime = n + 1         # Find next prime number    while not isPrime(next_prime):        next_prime += 1             # Find previous prime number    while not isPrime(previous_prime):        previous_prime -= 1             # Arithmetic mean    mean = (previous_prime +            next_prime) / 2         # If n is a weak prime    if n == mean:        return True    else:        return False # Driver coden = 53 if isBalancedPrime(n):    print("Yes")else:    print("No") # This code is contributed by stutipathak31jan

## C#

 // C# program to check if a// given number is Balanced  primeusing System; class GFG {     // Utility 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;    }     // Function that returns true    // if n is a Balanced prime    static bool isBalancedPrime(int n)    {         // If n is not a prime number or        // n is the first prime then return false        if (!isPrime(n) || n == 2)            return false;         // Initialize previous_prime to n - 1        // and next_prime to n + 1        int previous_prime = n - 1;        int next_prime = n + 1;         // Find next prime number        while (!isPrime(next_prime))            next_prime++;         // Find previous prime number        while (!isPrime(previous_prime))            previous_prime--;         // Arithmetic mean        int mean = (previous_prime                    + next_prime)                   / 2;         // If n is a weak prime        if (n == mean)            return true;        else            return false;    }     // Driver code    public static void Main()    {        int n = 53;         if (isBalancedPrime(n))            Console.WriteLine("Yes");        else            Console.WriteLine("No");    }}

## Javascript

 
Output:
Yes

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