Print all multiplicative primes <= N

Given an integer N, the task is to print all the multiplicative primes ≤ N.

Multiplicative Primes are the primes such that the product of their digits is also a prime. For example; 2, 3, 7, 13, 17, …

Examples:

Input: N = 10
Output: 2 3 5 7

Input: N = 3
Output: 2 3

Approach: Using Sieve of Eratosthenes check for all the primes ≤ N whether they are multiplicative primes i.e. product of their digits is also a prime. If yes then print those multiplicative primes.

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the digit product of n
int digitProduct(int n)
{
    int prod = 1;
    while (n) {
        prod = prod * (n % 10);
        n = n / 10;
    }
  
    return prod;
}
  
// Function to print all multiplicative primes <= n
void printMultiplicativePrimes(int n)
{
    // Create a boolean array "prime[0..n+1]". A
    // value in prime[i] will finally be false
    // if i is Not a prime, else true.
    bool prime[n + 1];
    memset(prime, true, sizeof(prime));
  
    prime[0] = prime[1] = false;
    for (int p = 2; p * p <= n; p++) {
  
        // If prime[p] is not changed, then
        // it is a prime
        if (prime[p]) {
  
            // Update all multiples of p
            for (int i = p * 2; i <= n; i += p)
                prime[i] = false;
        }
    }
  
    for (int i = 2; i <= n; i++) {
  
        // If i is prime and its digit sum is also prime
        // i.e. i is a multiplicative prime
        if (prime[i] && prime[digitProduct(i)])
            cout << i << " ";
    }
}
  
// Driver code
int main()
{
    int n = 10;
    printMultiplicativePrimes(n);
}

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Java

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// Java implementation of the approach
import java.io.*;
  
class GFG 
{
  
// Function to return the digit product of n
static int digitProduct(int n)
{
    int prod = 1;
    while (n > 0
    {
        prod = prod * (n % 10);
        n = n / 10;
    }
    return prod;
}
  
// Function to print all multiplicative primes <= n
static void printMultiplicativePrimes(int n)
{
    // Create a boolean array "prime[0..n+1]". A
    // value in prime[i] will finally be false
    // if i is Not a prime, else true.
    boolean prime[] = new boolean[n + 1 ];
    for(int i = 0; i <= n; i++)
     prime[i] = true;
  
    prime[0] = prime[1] = false;
    for (int p = 2; p * p <= n; p++) 
    {
  
        // If prime[p] is not changed, then
        // it is a prime
        if (prime[p]) 
        {
  
            // Update all multiples of p
            for (int i = p * 2; i <= n; i += p)
                prime[i] = false;
        }
    }
  
    for (int i = 2; i <= n; i++)
    {
  
        // If i is prime and its digit sum is also prime
        // i.e. i is a multiplicative prime
        if (prime[i] && prime[digitProduct(i)])
            System.out.print( i + " ");
    }
}
  
    // Driver code
    public static void main (String[] args) 
    {
        int n = 10;
        printMultiplicativePrimes(n);
    }
}
  
// This code is contributed by shs..

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Python3

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# Python 3 implementation of the approach
from math import sqrt
  
# Function to return the digit product of n
def digitProduct(n):
    prod = 1
    while (n):
        prod = prod * (n % 10)
        n = int(n / 10)
  
    return prod
  
# Function to print all multiplicative
# primes <= n
def printMultiplicativePrimes(n):
      
    # Create a boolean array "prime[0..n+1]". 
    # A value in prime[i] will finally be 
    # false if i is Not a prime, else true.
    prime = [True for i in range(n + 1)]
  
    prime[0] = prime[1] = False
    for p in range(2, int(sqrt(n)) + 1, 1):
          
        # If prime[p] is not changed, 
        # then it is a prime
        if (prime[p]):
              
            # Update all multiples of p
            for i in range(p * 2, n + 1, p):
                prime[i] = False
          
    for i in range(2, n + 1, 1):
          
        # If i is prime and its digit sum 
        # is also prime i.e. i is a
        # multiplicative prime
        if (prime[i] and prime[digitProduct(i)]):
            print(i, end = " ")
  
# Driver code
if __name__ == '__main__':
    n = 10
    printMultiplicativePrimes(n)
  
# This code is contributed by
# Surendra_Gangwar

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C#

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// C# implementation of the approach
class GFG 
{
  
// Function to return the digit product of n
static int digitProduct(int n)
{
    int prod = 1;
    while (n > 0) 
    {
        prod = prod * (n % 10);
        n = n / 10;
    }
    return prod;
}
  
// Function to print all multiplicative primes <= n
static void printMultiplicativePrimes(int n)
{
    // Create a boolean array "prime[0..n+1]". A
    // value in prime[i] will finally be false
    // if i is Not a prime, else true.
    bool[] prime = new bool[n + 1 ];
      
    for(int i = 0; i <= n; i++)
        prime[i] = true;
  
    prime[0] = prime[1] = false;
    for (int p = 2; p * p <= n; p++) 
    {
  
        // If prime[p] is not changed, then
        // it is a prime
        if (prime[p]) 
        {
  
            // Update all multiples of p
            for (int i = p * 2; i <= n; i += p)
                prime[i] = false;
        }
    }
  
    for (int i = 2; i <= n; i++)
    {
  
        // If i is prime and its digit sum is also prime
        // i.e. i is a multiplicative prime
        if (prime[i] && prime[digitProduct(i)])
            System.Console.Write( i + " ");
    }
}
  
    // Driver code
    static void Main() 
    {
        int n = 10;
        printMultiplicativePrimes(n);
    }
}
  
// This code is contributed by chandan_jnu

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PHP

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<?php
// PHP implementation of the approach
  
// Function to return the digit product of n
function digitProduct($n)
{
    $prod = 1;
    while ($n
    {
        $prod = $prod * ($n % 10);
        $n = floor($n / 10);
    }
  
    return $prod;
}
  
// Function to print all multiplicative
// primes <= n
function printMultiplicativePrimes($n)
{
    // Create a boolean array "prime[0..n+1]". 
    // A value in prime[i] will finally be 
    // false if i is Not a prime, else true.
    $prime = array_fill(0, $n + 1, true);
      
    $prime[0] = $prime[1] = false;
    for ($p = 2; $p * $p <= $n; $p++) 
    {
  
        // If prime[p] is not changed, then
        // it is a prime
        if ($prime[$p]) 
        {
  
            // Update all multiples of p
            for ($i = $p * 2; $i <= $n; $i += $p)
                $prime[$i] = false;
        }
    }
  
    for ($i = 2; $i <= $n; $i++) 
    {
  
        // If i is prime and its digit sum is also 
        // prime i.e. i is a multiplicative prime
        if ($prime[$i] && $prime[digitProduct($i)])
            echo $i, " ";
    }
}
  
// Driver code
$n = 10;
printMultiplicativePrimes($n);
  
// This code is contributed by Ryuga.
?>

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Output:

2 3 5 7


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