Given a positive integer N, the task is to check whether the given number is good prime or not. If the given number is good prime print ‘YES’ Otherwise Print ‘NO’.
Good Prime: In Mathematics, a good prime is a prime number whose square is greater than the product of any two primes at the same number of positions before and after it in the sequence of primes. In other word, A prime Pn is said to be good prime if it for every 1 <= i < n.
The first few good primes are: 5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 97, 101, 127, 149, 179, 191, 223, ….
Input: N = 5
Explanation: 5 is a good prime number
since 5^2 = 25 is greater than 3.7 = 21
and 2.11 = 22.
Input: N = 20
1. Get the number N.
2. Initialise prev_prime = N-1 and next_prime = N+1
3. Iterate the loop while prev_prime is greater than or equal to 2. And check for both next_prime and prev_prime are prime of not using prime number.
4. If both are not prime, then repeat step 2 and 3.
5. If both next_prime and prev_prime are prime, then check N^2 > next_prime . prev_prime or not.
- If Not then number is not good prime and stop the execution and return NO.
- If Yes then repeat the step 2, 3, 4 and 5.
Below is the implementaion of the above approach:
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