# Sum of prime numbers without odd prime digits

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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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 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 ans = ``new` `Vector(); ` `     `  `    ``// 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 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 `

Output :

`252`

My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Article Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.