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……
Input: N = 5
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
- 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:
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