# Check if N is a Balanced Prime number or not

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

In number theory, a

Balanced Primeis 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 = 5Output:Yes5 is 3rd prime number, the arithmetic mean of 2nd and 4th prime number i.e. 3 and 7 is 5.so 5 is aBalancedprime.

Input:N = 11Output: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**.

- If

Below is the implementation of the above approach:

## C#

`// C# program to check if a ` `// given number is Balanced prime ` `using` `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"` `); ` ` ` `} ` `}` |

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**Output:**

Yes

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