Número primo de Chen

Posted on by Rudeus Greyrat

Dado un entero positivo n, la tarea es verificar si es un número primo de Chen. Si el número dado es un número Chen Prime, imprima ‘SÍ’; de lo contrario, imprima ‘NO’.
Número primo de Chen : en matemáticas, un número primo ‘p’ se denomina número primo de Chen , si ‘p+2’ es un número primo o un número semiprimo. 
Un número semiprimo es el producto de dos números primos.
Los primeros números primos de Chen son: 
 

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

Ejemplos: 
 

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

requisito previo : 
 

Acercarse: 
 

  1. Comprueba si el número dado – ‘n’ es primo o no.
  2. Si n es un número primo:
    • Comprobar si n+2 es primo o semiprimo
    • Imprime ‘SÍ’ si n+2 es un número primo o un número semiprimo
    • De lo contrario, escriba ‘NO’
  3. Si n no es un número primo, imprima ‘NO’.
     

A continuación se muestra la implementación de la idea anterior.
 

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>
Producción: 

YES

 

Publicación traducida automáticamente

Artículo escrito por ihritik y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA

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