Check whether a number is Good prime or not

14 May, 2021
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, ....
Examples:
Input: N = 5 Output: YES Explanation: 5 is a good prime number since 5^2 = 25 is greater than 3.7 = 21 and 2.11 = 22.  
Input:  N = 20 Output: NO 
Approach:
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 implementation of the above approach:
C++
Java
Python3
C#
Javascript
// C++ program to check if a number// is good prime or not#include<bits/stdc++.h>using namespace std; // 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 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 to check if the// given number is Good primebool isGoodprime (int n){     // Smallest good prime is 5    // So the number less than 5    // can not be a Good prime     if (n < 5)        return false;     int prev_prime = n - 1;    int next_prime = n + 1;     while (prev_prime >= 2)    {                 // Calculate first prime number < n        while (!isPrime(prev_prime))        {            prev_prime--;        }         // Calculate first prime number > n        while (!isPrime(next_prime))        {            next_prime++;        }         // Check if product of next_prime        // and prev_prime is less than n^2        if ((prev_prime * next_prime) >= n * n)            return false;         prev_prime -= 1;        next_prime += 1;    }    return true;} // Driver codeint main(){    int n = 11;     if (isGoodprime(n))        cout << "YES";    else        cout << "NO";     return 0;} // This code is contributed by himanshu77
// Java program to check if a number is// good prime or notclass GFG{ // Function to check if a// number is prime or notstatic 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 = i + 6)    {       if (n % i == 0 || n % (i + 2) == 0)       {           return false;       }    }    return true;} // Function to check if the given// number is good prime or notstatic boolean isGoodrprime(int n){     // Smallest good prime is 5    // So the number less than 5    // can not be a good prime     if (n < 5)        return false;     int prev_prime = n - 1;    int next_prime = n + 1;     while (prev_prime >= 2)    {                 // Calculate first prime number < n        while (!isPrime(prev_prime))        {            prev_prime--;        }         // Calculate first prime number > n        while (!isPrime(next_prime))        {            next_prime++;        }         // Check if product of next_prime        // and prev_prime        // is less than n^2        if ((prev_prime * next_prime) >= n * n)            return false;         prev_prime -= 1;        next_prime += 1;    }    return true;} // Driver codepublic static void main(String []args){    int n = 11;         if (isGoodrprime(n))        System.out.println("YES");    else        System.out.println("NO");}} // This code is contributed by amal kumar choubey
# Python3 program to check if a number is# good prime or not # 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 = i + 6    return True # Function to check if the given number# is good prime or notdef isGoodrPrime(n):     # Declaring variables as global    global next_prime, prev_prime     # Smallest good prime is 5    # So the number less than 5    # can not be a good prime    if(n < 5):        return False     # Initialize previous_prime to n - 1    # and next_prime to n + 1    prev_prime = n - 1    next_prime = n + 1     while(prev_prime >= 2):         # Calculate first prime number < n        while (not isPrime(prev_prime)):            prev_prime -= 1         # Calculate first prime number > n        while(not isPrime(next_prime)):            next_prime += 1         # Check if product of next_prime        # and prev_prime        # is less than n^2        if((prev_prime * next_prime) >= n * n):            return False         prev_prime -= 1        next_prime += 1     return True # Driver codeif __name__ == '__main__':     n = 11     if(isGoodrPrime(n)):        print("Yes")    else:        print("No") # This code is contributed by Shivam Singh
// C# program to check if a number is// good prime  or not using System;class GFG {     // 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 to check    // if the given number is good prime or not    static bool isGoodrprime(int n)    {         // Smallest good prime is 5        // So the number less than 5        // can not be a good prime         if (n < 5)            return false;         int prev_prime = n - 1;        int next_prime = n + 1;         while (prev_prime >= 2) {            // Calculate first prime number < n            while (!isPrime(prev_prime)) {                prev_prime--;            }             // Calculate first prime number > n            while (!isPrime(next_prime)) {                next_prime++;            }             // check if product of next_prime            // and prev_prime            // is less than n^2             if ((prev_prime * next_prime)                >= n * n)                return false;             prev_prime -= 1;            next_prime += 1;        }        return true;    }     public static void Main()    {         int n = 11;        if (isGoodrprime(n))            Console.WriteLine("YES");        else            Console.WriteLine("NO");    }}
<script> // Javascript program to check if a number// is good prime or not // Function to check if a// number is Prime or notfunction 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 loop    if (n % 2 == 0 || n % 3 == 0)        return false;     for(let i = 5; i * i <= n; i += 6)    {    if (n % i == 0 || n % (i + 2) == 0)        return false;    }    return true;} // Function to check if the// given number is Good prime function isGoodprime (n){     // Smallest good prime is 5    // So the number less than 5    // can not be a Good prime     if (n < 5)        return false;     let prev_prime = n - 1;    let next_prime = n + 1;     while (prev_prime >= 2)    {                 // Calculate first prime number < n        while (!isPrime(prev_prime))        {            prev_prime--;        }         // Calculate first prime number > n        while (!isPrime(next_prime))        {            next_prime++;        }         // Check if product of next_prime        // and prev_prime is less than n^2        if ((prev_prime * next_prime) >= n * n)            return false;         prev_prime -= 1;        next_prime += 1;    }    return true;} // Driver code     let n = 11;     if (isGoodprime(n))        document.write("YES");    else        document.write("NO");  // This code is contributed by Mayank Tyagi </script>
YES
 
Time Complexity: O(n3/2)
Auxiliary Space: O(1)
SHIVAMSINGH67
Amal Kumar Choubey
himanshu77
subhammahato348
mayanktyagi1709
arorakashish0911
Prime Number
Mathematical
Mathematical
Prime Number
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