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Chen Prime Number

  • Last Updated : 11 May, 2021

Given a positive integer n, the task is to check if it is a Chen prime number. If the given number is a Chen Prime number then print ‘YES’ otherwise print ‘NO’.
Chen prime Number: In mathematics, a Prime number ‘p’ is called as chen prime number , if either ‘p+2’ is a prime number or a semi prime number. 
A semi-prime number is product of two prime numbers.
The first few Chen prime numbers are: 
 

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101 
 

Examples: 
 

Input : 11
Output: YES
Explanation: 11 is prime number and 11+2 
(i.e 13 is also prime number)

Input : 7
Output: YES
Explanation: 7 is prime number and 7+2 
( i.e 9 ) is a semi prime number 

 

Prerequisite
 

Approach: 
 

  1. Check if the given number – ‘n’ is a prime or not.
  2. If n is a prime number:
    • Check if n+2 is either prime or semi-prime
    • Print ‘YES’ if n+2 is either prime number or a semi-prime number
    • Otherwise print ‘NO’
  3. If n is not a prime number, print ‘NO’.
     

Below is the implementation of the above idea
 

CPP




// CPP program to check
// Chen prime number
 
#include <bits/stdc++.h>
using namespace std;
 
// Utility function to check whether
// number is semiprime or not
int isSemiprime(int num)
{
    int cnt = 0;
 
    for (int i = 2; cnt < 2 && i * i <= num; ++i)
        while (num % i == 0)
            num /= i, ++cnt; // Increment count
    // of prime numbers
 
    // If number is greater than 1, add it to
    // the count variable as it indicates the
    // number remain is prime number
    if (num > 1)
        ++cnt;
 
    // Return '1' if count is equal to '2' else
    // return '0'
    return cnt == 2;
}
 
// Utility function to check whether
// the given number is prime or not
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 Chen prime number
bool isChenPrime(int n)
{
 
    if (isPrime(n) && (isSemiprime(n + 2) || isPrime(n + 2)))
        return true;
    else
        return false;
}
 
// Driver code
int main()
{
    int n = 7;
 
    if (isChenPrime(n))
        cout << "YES";
    else
        cout << "NO";
 
    return 0;
}

Java




// JAVA program to check
// Chen Prime number
 
class GFG {
    // Utility function to check
    // if the given number is semi-prime or not
    static boolean isSemiPrime(int num)
    {
        int cnt = 0;
 
        for (int i = 2; cnt < 2 && i * i <= num; ++i)
 
            while (num % i == 0) {
                num /= i;
 
                // Increment count
                // of prime numbers
                ++cnt;
            }
 
        // If number is greater than 1,
        // add it to the count variable
        // as it indicates the number
        // remain is prime number
        if (num > 1)
            ++cnt;
 
        // Return '1' if count is equal
        // to '2' else return '0'
        return cnt == 2 ? true : false;
    }
 
    // 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 = i + 6) {
            if (n % i == 0 || n % (i + 2) == 0) {
                return false;
            }
        }
        return true;
    }
 
    // Function to check chen prime number
    static boolean isChenPrime(int n)
    {
 
        if (isPrime(n) && (isSemiPrime(n + 2) || isPrime(n + 2)))
            return true;
        else
            return false;
    }
    // Driver code
    public static void main(String[] args)
    {
 
        int n = 7;
 
        if (isChenPrime(n))
            System.out.println("YES");
        else
            System.out.println("NO");
    }
}

C#




// C# program to check
// Chen Prime number
using System;
class GFG {
    // Utility function to check
    // if the given number is semi-prime or not
    static bool isSemiPrime(int num)
    {
        int cnt = 0;
 
        for (int i = 2; cnt < 2 && i * i <= num; ++i)
 
            while (num % i == 0) {
                num /= i;
 
                // Increment count
                // of prime numbers
                ++cnt;
            }
 
        // If number is greater than 1,
        // add it to the count variable
        // as it indicates the number
        // remain is prime number
        if (num > 1)
            ++cnt;
 
        // Return '1' if count is equal
        // to '2' else return '0'
        return cnt == 2 ? true : false;
    }
 
    // 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 chen prime number
    static bool isChenPrime(int n)
    {
 
        if (isPrime(n) && (isSemiPrime(n + 2) || isPrime(n + 2)))
            return true;
        else
            return false;
    }
    // Driver code
    public static void Main()
    {
 
        int n = 7;
 
        if (isChenPrime(n))
            Console.WriteLine("YES");
        else
            Console.WriteLine("NO");
    }
}

Python3




# Python3 program to check
# Chen Prime number
 
import math
         
# Utility function to Check
# Semi-prime number
 
def isSemiPrime(num):
    cnt = 0
   
    for i in range(2, int(math.sqrt(num)) + 1):
        while num % i == 0:
            num /= i
            cnt += 1 # Increment count
                    # of prime number
   
        # If count is greater than 2,
        # break loop 
        if cnt >= 2
            break
    # If number is greater than 1, add it to
    # the count variable as it indicates the
    # number remain is prime number
    if(num > 1):
        cnt += 1
   
    # Return '1' if count is equal to '2' else
    # return '0'
    return cnt == 2
  
  
 
# Utility function to check 
# if a number is prime or not 
def 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 Chen prime number or not
         
def isChenPrime( n):
 
    if(isPrime(n) and (isSemiPrime(n + 2) or isPrime(n + 2))):
        return True
    else:
        return False
             
# Driver code
 
n = 7
 
if(isChenPrime(n)):
    print("YES");
else:
    print("NO");
    

Javascript




<script>
 
// Javascript program to check
// Chen prime number
 
// Utility function to check whether
// number is semiprime or not
function isSemiprime(num)
{
    var cnt = 0;
 
    for (var i = 2; cnt < 2 && i * i <= num; ++i)
        while (num % i == 0)
            num /= i, ++cnt; // Increment count
    // of prime numbers
 
    // If number is greater than 1, add it to
    // the count variable as it indicates the
    // number remain is prime number
    if (num > 1)
        ++cnt;
 
    // Return '1' if count is equal to '2' else
    // return '0'
    return cnt == 2;
}
 
// Utility function to check whether
// the given number is prime or not
function 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 || n % 3 == 0)
        return false;
 
    for (var i = 5; i * i <= n; i = i + 6) {
        if (n % i == 0 || n % (i + 2) == 0) {
            return false;
        }
    }
 
    return true;
}
 
// Function to check Chen prime number
function isChenPrime(n)
{
 
    if (isPrime(n) && (isSemiprime(n + 2) || isPrime(n + 2)))
        return true;
    else
        return false;
}
 
// Driver code
var n = 7;
if (isChenPrime(n))
    document.write( "YES");
else
    document.write( "NO");
 
// This code is contributed by noob2000.
</script>
Output: 
YES

 


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