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Sum of prime numbers without odd prime digits

  • Last Updated : 11 May, 2021

Given an integer N. The task is to find the sum of the first N prime numbers which don’t contain any odd primes as their digit.
Some of such prime numbers are 2, 11, 19, 29, 41 …… 
Examples: 
 

Input : N = 2 
Output : 13 
2 + 11 = 13
Input : N = 7 
Output : 252 
 

 

Approach :
 

  • We first use a Sieve of Eratosthenes to store all prime numbers.
  • Next check for each prime number if any odd prime digit is present or not.
  • If no such digit is present then we will include this prime to our required answer
  • Continue above step until we get N such prime numbers

Below is the implementation of the above approach : 
 

C++




#include <bits/stdc++.h>
using namespace std;
 
#define MAX 100005
 
// Find all prime numbers
vector<int> addPrimes()
{
    int n = MAX;
 
    bool prime[n + 1];
    memset(prime, true, sizeof(prime));
 
    for (int p = 2; p * p <= n; p++) {
 
        if (prime[p] == true) {
            for (int i = p * p; i <= n; i += p)
                prime[i] = false;
        }
    }
    vector<int> ans;
    // Store all prime numbers
    for (int p = 2; p <= n; p++)
        if (prime[p])
            ans.push_back(p);
 
    return ans;
}
 
// Function to check if a digit is odd prime or not
bool is_prime(int n)
{
    return (n == 3 || n == 5 || n == 7);
}
 
// Function to find sum
int find_Sum(int n)
{
    // To store required answer
    int sum = 0;
     
    // Get all prime numbers
    vector<int> v = addPrimes();
     
    // Traverse through all the prime numbers
    for (int i = 0; i < v.size() and n; i++)
    {
        // Flag stores 1 if a number does
        // not contain any odd primes
        int flag = 1;
        int a = v[i];
         
        // Find all digits of a number
        while (a != 0)
        {
            int d = a % 10;
            a = a / 10;
            if (is_prime(d)) {
                flag = 0;
                break;
            }
        }
         
        // If number does not contain any odd primes
        if (flag==1)
        {
            n--;
            sum = sum + v[i];
        }
    }
 
    // Return the required answer
    return sum;
}
 
// Driver code
int main()
{
    int n = 7;
     
    // Function call
    cout << find_Sum(n);
 
    return 0;
}

Java




// Java program for above approach
import java.util.*;
 
class GFG
{
static int MAX = 100005;
 
// Find all prime numbers
static Vector<Integer> addPrimes()
{
    int n = MAX;
 
    boolean []prime = new boolean[n + 1];
    Arrays.fill(prime, true);
 
    for (int p = 2; p * p <= n; p++)
    {
        if (prime[p] == true)
        {
            for (int i = p * p; i <= n; i += p)
                prime[i] = false;
        }
    }
    Vector<Integer> ans = new Vector<Integer>();
     
    // Store all prime numbers
    for (int p = 2; p <= n; p++)
        if (prime[p])
            ans.add(p);
 
    return ans;
}
 
// Function to check if a digit
// is odd prime or not
static boolean is_prime(int n)
{
    return (n == 3 || n == 5 || n == 7);
}
 
// Function to find sum
static int find_Sum(int n)
{
    // To store required answer
    int sum = 0;
     
    // Get all prime numbers
    Vector<Integer> v = addPrimes();
     
    // Traverse through all the prime numbers
    for (int i = 0; i < v.size() && n > 0; i++)
    {
        // Flag stores 1 if a number does
        // not contain any odd primes
        int flag = 1;
        int a = v.get(i);
         
        // Find all digits of a number
        while (a != 0)
        {
            int d = a % 10;
            a = a / 10;
            if (is_prime(d))
            {
                flag = 0;
                break;
            }
        }
         
        // If number does not contain
        // any odd primes
        if (flag == 1)
        {
            n--;
            sum = sum + v.get(i);
        }
    }
 
    // Return the required answer
    return sum;
}
 
// Driver code
public static void main(String[] args)
{
    int n = 7;
     
    // Function call
    System.out.println(find_Sum(n));
}
}
 
// This code is contributed by 29AjayKumar

Python3




# Python3 program for above approach
MAX = 100005
 
def addPrimes():
    n = MAX
 
    prime = [True for i in range(n + 1)]
 
    for p in range(2, n + 1):
 
        if p * p > n:
            break
 
        if (prime[p] == True):
            for i in range(2 * p, n + 1, p):
                prime[i] = False
 
    ans = []
     
    # Store all prime numbers
    for p in range(2, n + 1):
        if (prime[p]):
            ans.append(p)
 
    return ans
 
# Function to check if
# a digit is odd prime or not
def is_prime(n):
    if n in [3, 5, 7]:
        return True
    return False
 
# Function to find sum
def find_Sum(n):
     
    # To store required answer
    Sum = 0
 
    # Get all prime numbers
    v = addPrimes()
 
    # Traverse through all the prime numbers
    for i in range(len(v)):
         
        # Flag stores 1 if a number does
        # not contain any odd primes
        flag = 1
        a = v[i]
 
        # Find all digits of a number
        while (a != 0):
 
            d = a % 10;
            a = a // 10;
            if (is_prime(d)):
                flag = 0
                break
 
        # If number does not contain any odd primes
        if (flag == 1):
            n -= 1
            Sum = Sum + v[i]
        if n == 0:
            break
 
    # Return the required answer
    return Sum
 
# Driver code
n = 7
 
# Function call
print(find_Sum(n))
 
# This code is contributed by Mohit Kumar

C#




// C# program for above approach
using System;
using System.Collections.Generic;
 
class GFG
{
static int MAX = 100005;
 
// Find all prime numbers
static List<int> addPrimes()
{
    int n = MAX;
 
    Boolean []prime = new Boolean[n + 1];
    for(int i = 0; i < n + 1; i++)
        prime[i]=true;
 
    for (int p = 2; p * p <= n; p++)
    {
        if (prime[p] == true)
        {
            for (int i = p * p; i <= n; i += p)
                prime[i] = false;
        }
    }
    List<int> ans = new List<int>();
     
    // Store all prime numbers
    for (int p = 2; p <= n; p++)
        if (prime[p])
            ans.Add(p);
 
    return ans;
}
 
// Function to check if a digit
// is odd prime or not
static Boolean is_prime(int n)
{
    return (n == 3 ||
            n == 5 || n == 7);
}
 
// Function to find sum
static int find_Sum(int n)
{
    // To store required answer
    int sum = 0;
     
    // Get all prime numbers
    List<int> v = addPrimes();
     
    // Traverse through all the prime numbers
    for (int i = 0;
             i < v.Count && n > 0; i++)
    {
        // Flag stores 1 if a number does
        // not contain any odd primes
        int flag = 1;
        int a = v[i];
         
        // Find all digits of a number
        while (a != 0)
        {
            int d = a % 10;
            a = a / 10;
            if (is_prime(d))
            {
                flag = 0;
                break;
            }
        }
         
        // If number does not contain
        // any odd primes
        if (flag == 1)
        {
            n--;
            sum = sum + v[i];
        }
    }
 
    // Return the required answer
    return sum;
}
 
// Driver code
public static void Main(String[] args)
{
    int n = 7;
     
    // Function call
    Console.WriteLine(find_Sum(n));
}
}
 
// This code is contributed by Princi Singh

Javascript




<script>
 
const MAX = 100005;
 
// Find all prime numbers
function addPrimes()
{
    let n = MAX;
 
    let prime = new Array(n + 1).fill(true);
 
    for (let p = 2; p * p <= n; p++) {
 
        if (prime[p] == true) {
            for (let i = p * p; i <= n; i += p)
                prime[i] = false;
        }
    }
    let ans = [];
    // Store all prime numbers
    for (let p = 2; p <= n; p++)
        if (prime[p])
            ans.push(p);
 
    return ans;
}
 
// Function to check if a digit is odd prime or not
function is_prime(n)
{
    return (n == 3 || n == 5 || n == 7);
}
 
// Function to find sum
function find_Sum(n)
{
    // To store required answer
    let sum = 0;
     
    // Get all prime numbers
    let v = addPrimes();
     
    // Traverse through all the prime numbers
    for (let i = 0; i < v.length && n > 0; i++)
    {
        // Flag stores 1 if a number does
        // not contain any odd primes
        let flag = 1;
        let a = v[i];
         
        // Find all digits of a number
        while (a != 0)
        {
            let d = a % 10;
            a = parseInt(a / 10);
            if (is_prime(d)) {
                flag = 0;
                break;
            }
        }
         
        // If number does not contain any odd primes
        if (flag==1)
        {
            n--;
            sum = sum + v[i];
        }
    }
 
    // Return the required answer
    return sum;
}
 
// Driver code
    let n = 7;
     
    // Function call
    document.write(find_Sum(n));
 
</script>

Output : 
 

252

 


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