Additive Prime Number

Given a number N, the task is to check if N is an Additive Prime Number or not. If N is an Additive Prime Number then print “Yes” else print “No”.

An Additive Prime Number is a prime number P such that the sum of digits of P is also a prime number. 
For example, 23 is an Additive prime because 2 + 3 = 5 which is a prime number. 

Examples:

Input: N = 23 
Output: Yes 
Explanation: Sum of digits of 23 = 2 + 3 = 5.

Input: N = 10 
Output: No 

Approach: The idea is to find the sum of digits of the number N and check if it is prime or not. If the sum is a prime number then print “Yes” else print “No”.

Algorithm:

• Define a function named isPrime that takes an integer as input and returns true if it is a prime number, and false otherwise.
• Check if the input number is less than or equal to 1. If yes, return false.
• Use a for loop to iterate from 2 to the square root of the input number. If the input number is divisible by any number in this range, return false. Otherwise, return true.
• Define a function named digit_sum that takes an integer as input and returns the sum of its digits.
• Initialize a variable ans to 0.
• Use a while loop to iterate as long as the input number is greater than 0.
• Add the last digit of the input number to ans and remove the last digit from the input number.
• Return ans.
• Define a function named additive_prime that takes an integer as input and returns 1 if it is an additive prime, and 0 otherwise.
• Check if the input number is a prime number using the isPrime function.
• If the input number is a prime number, calculate the sum of its digits using the digit_sum function.
• Check if the sum of digits is a prime number using the isPrime function.
• If both the input number and its sum of digits are prime numbers, return 1. Otherwise, return 0.
• In the main function:

                    a. Define an integer variable.

                    b. Call the additive_prime function with the integer variable as an argument.

                    c. If the function returns 1, print “Yes” to the console. Otherwise, print “No”.

• End of the program.

Below is the implementation of the above approach: 

C++

#include <iostream>
using namespace std;

// Function to check whether a number is prime or not.
bool isPrime(int n)
{
    // Corner cases
    if (n <= 1)
        return false;
  //suppose n=7 that is prime and its pair are (1,7)
  //so if a no. is prime then it can be check by numbers smaller than square root
  // of the n
    for (int i = 2; i * i <= n; i++) {
        if (n % i == 0)
            return false;
    }
    return true;
}

// Function to find the sum of the digits of a number.
int digit_sum(int n)
{
    int ans = 0;
    while (n > 0) {
        ans += (n % 10);
        n /= 10;
    }
    return ans;
}

// Function to check whether a number is additive prime or
// not.
int additive_prime(int n)
{
    if (isPrime(n)) {
        int d_sum = digit_sum(n);
        if (isPrime(d_sum))
            return 1;
    }
    return 0;
}

// Driver Code
int main()
{

    int n = 23;

    // Function Call
    if (additive_prime(n))
        cout << "Yes" << endl;
    else
        cout << "No" << endl;
    return 0;
}

Java

import java.util.*;

public class Gfg {

  // Function to check whether a number is prime or not.
  public static boolean isPrime(int n)
  {

    // Corner cases
    if (n <= 1) {
      return false;
    }

    // Suppose n=7 that is prime and its pair are (1,7)
    // So if a no. is prime then it can be check by numbers smaller than square root
    // of the n
    for (int i = 2; i * i <= n; i++) {
      if (n % i == 0) {
        return false;
      }
    }
    return true;
  }

  // Function to find the sum of the digits of a number.
  public static int digit_sum(int n) {
    int ans = 0;
    while (n > 0) {
      ans += (n % 10);
      n /= 10;
    }
    return ans;
  }

  // Function to check whether a number is additive prime or not.
  public static int additive_prime(int n) {
    if (isPrime(n)) {
      int d_sum = digit_sum(n);
      if (isPrime(d_sum)) {
        return 1;
      }
    }
    return 0;
  }

  // Driver Code
  public static void main(String[] args) {
    int n = 23;

    // Function Call
    if (additive_prime(n) == 1) {
      System.out.println("Yes");
    } else {
      System.out.println("No");
    }
  }
}

Python

# Python Equivalent

# Function to check whether a number is prime or not.
def isPrime(n):
    # Corner cases
    if (n <= 1):
        return False
    #suppose n=7 that is prime and its pair are (1,7)
    #so if a no. is prime then it can be check by numbers smaller than square root
    # of the n
    for i in range(2, int(n**0.5) + 1):
        if (n % i == 0):
            return False
    return True

# Function to find the sum of the digits of a number.
def digit_sum(n):
    ans = 0
    while (n > 0):
        ans += (n % 10)
        n = int(n/10)
    return ans

# Function to check whether a number is additive prime or
# not.
def additive_prime(n):
    if (isPrime(n)):
        d_sum = digit_sum(n)
        if (isPrime(d_sum)):
            return 1
    return 0

# Driver Code
if __name__ == '__main__':
    n = 23

    # Function Call
    if (additive_prime(n)):
        print("Yes")
    else:
        print("No")

C#

using System;

namespace AdditivePrime
{
  class Program
  {
    // Function to check whether a number is prime or not.
    static bool IsPrime(int n)
    {
      // Corner cases
      if (n <= 1) {
        return false;
      }
      // Suppose n=7 that is prime and its pair are (1,7)
      // so if a no. is prime then it can be checked by
      // numbers smaller than square root of the n
      for (int i = 2; i * i <= n; i++) {
        if (n % i == 0) {
          return false;
        }
      }

      return true;
    }

    // Function to find the sum of the digits of a number.
    static int DigitSum(int n)
    {
      int ans = 0;

      while (n > 0) {
        ans += (n % 10);
        n /= 10;
      }

      return ans;
    }

    // Function to check whether a number is additive prime
    // or not.
    static bool IsAdditivePrime(int n)
    {
      if (IsPrime(n)) {
        int dSum = DigitSum(n);

        if (IsPrime(dSum)) {
          return true;
        }
      }

      return false;
    }

    static void Main(string[] args)
    {
      int n = 23;

      // Function Call
      if (IsAdditivePrime(n)) {
        Console.WriteLine("Yes");
      }
      else {
        Console.WriteLine("No");
      }
    }
  }
}

// This code is contributed by user_dtewbxkn77n

Javascript

// Function to check whether a number is prime or not.
function isPrime(n) {
  // Corner cases
  if (n <= 1) {
    return false;
  }

  // Suppose n=7 that is prime and its pair are (1,7)
  // So if a no. is prime then it can be checked by numbers smaller than square root
  // of the n
  for (let i = 2; i * i <= n; i++) {
    if (n % i === 0) {
      return false;
    }
  }

  return true;
}

// Function to find the sum of the digits of a number.
function digit_sum(n) {
  let ans = 0;

  while (n > 0) {
    ans += n % 10;
    n = Math.floor(n / 10);
  }

  return ans;
}

// Function to check whether a number is additive prime or
// not.
function additive_prime(n) {
  if (isPrime(n)) {
    const d_sum = digit_sum(n);
    if (isPrime(d_sum)) {
      return 1;
    }
  }

  return 0;
}

// Driver Code
const n = 23;

if (additive_prime(n)) {
  console.log("Yes");
} else {
  console.log("No");
}

Output

Yes

Time complexity:  O(logn)
Auxiliary Space: O(1), as constant space is used.