Print prime numbers with prime sum of digits in an array

Given an array arr[] and the task is to print the additive primes in an array.
Additive primes: Primes such that the sum of their digits is also a prime, such as 2, 3, 7, 11, 23 are additive primes but not 13, 19, 31 etc.

Examples:

```Input: arr[] = {2, 4, 6, 11, 12, 18, 7}
Output: 2, 11, 7

Input: arr[] = {2, 3, 19, 13, 25, 7}
Output: 2, 3, 7
```

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

A simple approach is to traverse through all array elements. For every element check if it is Additive prime or not.

This above approach is fine when array is small or when array values are large. For large sized arrays having relatively small values, we use Sieve to store primes up to maximum element of the array. Then check if the current element is prime or not. If yes then check the sum of its digit is also prime or not. If yes then print that number.

Below is the implementation of the above approach:

C++

 `// C++ implementation of the above approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to store the primes ` `void` `sieve(``int` `maxEle, ``int` `prime[]) ` `{ ` `    ``prime[0] = prime[1] = 1; ` ` `  `    ``for` `(``int` `i = 2; i * i <= maxEle; i++) { ` `        ``if` `(!prime[i]) { ` `            ``for` `(``int` `j = 2 * i; j <= maxEle; j += i) ` `                ``prime[j] = 1; ` `        ``} ` `    ``} ` `} ` ` `  `// Function to return the sum of digits ` `int` `digitSum(``int` `n) ` `{ ` `    ``int` `sum = 0; ` `    ``while` `(n) { ` `        ``sum += n % 10; ` `        ``n = n / 10; ` `    ``} ` `    ``return` `sum; ` `} ` ` `  `// Function to print additive primes ` `void` `printAdditivePrime(``int` `arr[], ``int` `n) ` `{ ` ` `  `    ``int` `maxEle = *max_element(arr, arr + n); ` ` `  `    ``int` `prime[maxEle + 1]; ` `    ``memset``(prime, 0, ``sizeof``(prime)); ` `    ``sieve(maxEle, prime); ` ` `  `    ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `        ``// If the number is prime ` `        ``if` `(prime[arr[i]] == 0) { ` `            ``int` `sum = digitSum(arr[i]); ` ` `  `            ``// Check if it's digit sum is prime ` `            ``if` `(prime[sum] == 0) ` `                ``cout << arr[i] << ``" "``; ` `        ``} ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` ` `  `    ``int` `a[] = { 2, 4, 6, 11, 12, 18, 7 }; ` `    ``int` `n = ``sizeof``(a) / ``sizeof``(a[0]); ` ` `  `    ``printAdditivePrime(a, n); ` ` `  `    ``return` `0; ` `} `

Java

 `// Java implementation of the above approach ` `import` `java.util.Arrays; ` ` `  `class` `GFG ` `{ ` `     `  `// Function to store the primes ` `static` `void` `sieve(``int` `maxEle, ``int` `prime[]) ` `{ ` `    ``prime[``0``] = prime[``1``] = ``1``; ` ` `  `    ``for` `(``int` `i = ``2``; i * i <= maxEle; i++)  ` `    ``{ ` `        ``if` `(prime[i]==``0``) ` `        ``{ ` `            ``for` `(``int` `j = ``2` `* i; j <= maxEle; j += i) ` `                ``prime[j] = ``1``; ` `        ``} ` `    ``} ` `} ` ` `  `// Function to return the sum of digits ` `static` `int` `digitSum(``int` `n) ` `{ ` `    ``int` `sum = ``0``; ` `    ``while` `(n > ``0``)  ` `    ``{ ` `        ``sum += n % ``10``; ` `        ``n = n / ``10``; ` `    ``} ` `    ``return` `sum; ` `} ` ` `  `// Function to print additive primes ` `static` `void` `printAdditivePrime(``int` `arr[], ``int` `n) ` `{ ` ` `  `    ``int` `maxEle = Arrays.stream(arr).max().getAsInt(); ` ` `  `    ``int` `prime[] = ``new` `int``[maxEle + ``1``]; ` `    ``sieve(maxEle, prime); ` ` `  `    ``for` `(``int` `i = ``0``; i < n; i++)  ` `    ``{ ` ` `  `        ``// If the number is prime ` `        ``if` `(prime[arr[i]] == ``0``)  ` `        ``{ ` `            ``int` `sum = digitSum(arr[i]); ` ` `  `            ``// Check if it's digit sum is prime ` `            ``if` `(prime[sum] == ``0``) ` `                ``System.out.print(arr[i]+``" "``); ` `        ``} ` `    ``} ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` ` `  `    ``int` `a[] = { ``2``, ``4``, ``6``, ``11``, ``12``, ``18``, ``7` `}; ` `    ``int` `n =a.length; ` `    ``printAdditivePrime(a, n); ` `} ` `} ` ` `  `// This code is contributed by chandan_jnu `

Python3

 `# Python3 implementation of the  ` `# above approach  ` ` `  `# from math lib import sqrt ` `from` `math ``import` `sqrt ` ` `  `# Function to store the primes  ` `def` `sieve(maxEle, prime) : ` `     `  `    ``prime[``0``], prime[``1``] ``=` `1` `, ``1` ` `  `    ``for` `i ``in` `range``(``2``, ``int``(sqrt(maxEle)) ``+` `1``) : ` `        ``if` `(``not` `prime[i]) : ` `            ``for` `j ``in` `range``(``2` `*` `i , maxEle ``+` `1``, i) : ` `                ``prime[j] ``=` `1` `     `  `# Function to return the sum of digits  ` `def` `digitSum(n) :  ` `    ``sum` `=` `0` `    ``while` `(n) : ` `         `  `        ``sum` `+``=` `n ``%` `10` `        ``n ``=` `n ``/``/` `10` `    ``return` `sum` ` `  `# Function to print additive primes ` `def` `printAdditivePrime(arr, n): ` `    ``maxEle ``=` `max``(arr) ` `    ``prime ``=` `[``0``] ``*` `(maxEle ``+` `1``) ` `    ``sieve(maxEle, prime) ` `    ``for` `i ``in` `range``(n) : ` `         `  `        ``# If the number is prime ` `        ``if` `(prime[arr[i]] ``=``=` `0``): ` `            ``sum` `=` `digitSum(arr[i]) ` `             `  `            ``# Check if it's digit sum is prime ` `            ``if` `(prime[``sum``] ``=``=` `0``) : ` `                ``print``(arr[i], end ``=` `" "``)  ` `     `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `: ` `    ``a ``=` `[ ``2``, ``4``, ``6``, ``11``, ``12``, ``18``, ``7` `] ` `    ``n ``=` `len``(a) ` `    ``printAdditivePrime(a, n)  ` ` `  `# This code is contributed by Ryuga `

C#

 `// C# implementation of the above approach ` `using` `System.Linq; ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `// Function to store the primes ` `static` `void` `sieve(``int` `maxEle, ``int``[] prime) ` `{ ` `    ``prime[0] = prime[1] = 1; ` ` `  `    ``for` `(``int` `i = 2; i * i <= maxEle; i++)  ` `    ``{ ` `        ``if` `(prime[i] == 0) ` `        ``{ ` `            ``for` `(``int` `j = 2 * i; j <= maxEle; j += i) ` `                ``prime[j] = 1; ` `        ``} ` `    ``} ` `} ` ` `  `// Function to return the sum of digits ` `static` `int` `digitSum(``int` `n) ` `{ ` `    ``int` `sum = 0; ` `    ``while` `(n > 0)  ` `    ``{ ` `        ``sum += n % 10; ` `        ``n = n / 10; ` `    ``} ` `    ``return` `sum; ` `} ` ` `  `// Function to print additive primes ` `static` `void` `printAdditivePrime(``int` `[]arr, ``int` `n) ` `{ ` ` `  `    ``int` `maxEle = arr.Max(); ` ` `  `    ``int``[] prime = ``new` `int``[maxEle + 1]; ` `    ``sieve(maxEle, prime); ` ` `  `    ``for` `(``int` `i = 0; i < n; i++)  ` `    ``{ ` ` `  `        ``// If the number is prime ` `        ``if` `(prime[arr[i]] == 0)  ` `        ``{ ` `            ``int` `sum = digitSum(arr[i]); ` ` `  `            ``// Check if it's digit sum is prime ` `            ``if` `(prime[sum] == 0) ` `                ``Console.Write(arr[i] + ``" "``); ` `        ``} ` `    ``} ` `} ` ` `  `// Driver code ` `static` `void` `Main() ` `{ ` `    ``int``[] a = { 2, 4, 6, 11, 12, 18, 7 }; ` `    ``int` `n = a.Length; ` `    ``printAdditivePrime(a, n); ` `} ` `} ` ` `  `// This code is contributed by chandan_jnu `

PHP

Output:

```2 11 7
```

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