# Check whether the sum of prime elements of the array is prime or not

• Last Updated : 09 Sep, 2022

Given an array having N elements. The task is to check if the sum of prime elements of the array is prime or not.

Examples:

```Input: arr[] = {1, 2, 3}
Output: Yes
As there are two primes in the array i.e. 2 and 3.
So, the sum of prime is 2 + 3 = 5 and 5 is also prime.

Input: arr[] = {2, 3, 2, 2}
Output: No```

Approach: First find prime number up to 10^5 using Sieve. Then iterate over all elements of the array. If the number is prime then add it to sum. And finally, check whether the sum is prime or not. If prime then prints Yes otherwise No.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach` `#include ` `#define ll long long int` `#define MAX 100000` `using` `namespace` `std;` `bool` `prime[MAX];`   `// Sieve to find prime` `void` `sieve()` `{` `    ``memset``(prime, ``true``, ``sizeof``(prime));` `    ``prime[0] = prime[1] = ``false``;` `    ``for` `(``int` `i = 2; i < MAX; i++) ` `        ``if` `(prime[i]) ` `            ``for` `(``int` `j = 2 * i; j < MAX; j += i)` `                ``prime[j] = ``false``;` `        `  `    `  `}`   `// Function to check if the sum of` `// prime is prime or not` `bool` `checkArray(``int` `arr[], ``int` `n)` `{` `    ``// find sum of all prime number` `    ``ll sum = 0;` `    ``for` `(``int` `i = 0; i < n; i++)` `        ``if` `(prime[arr[i]])` `            ``sum += arr[i];`   `    ``// if sum is prime` `    ``// then return yes` `    ``if` `(prime[sum])` `        ``return` `true``;`   `    ``return` `false``;` `}`   `// Driver code` `int` `main()` `{` `    ``// array of elements` `    ``int` `arr[] = { 1, 2, 3 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);`   `    ``sieve();`   `    ``if` `(checkArray(arr, n))` `        ``cout << ``"Yes"``;` `    ``else` `        ``cout << ``"No"``;`   `    ``return` `0;` `}`

## Java

 `// Java implementation of the above approach` `import` `java.io.*;`   `class` `GFG {` `    `  `static` `int` `MAX =``100000``;`   `static` `boolean` `prime[] = ``new` `boolean``[MAX];`   `// Sieve to find prime` `static` `void` `sieve()` `{` `    ``for``(``int` `i=``0``;i

## Python3

 `# Python3 implementation of above approach` `from` `math ``import` `gcd, sqrt`   `MAX` `=` `100000`   `prime ``=` `[``True``] ``*` `MAX`   `# Sieve to find prime` `def` `sieve() :` `    `  `    ``# 0 and 1 are not prime numbers` `    ``prime[``0``] ``=` `False` `    ``prime[``1``] ``=` `False` `    `  `    ``for` `i ``in` `range``(``2``, ``MAX``) :`   `        ``if` `prime[i] :` `            ``for` `j ``in` `range``(``2``*``*``i, ``MAX``, i) :` `                ``prime[j] ``=` `False` `    `  `# Function to check if the sum of` `# prime is prime or not` `def` `checkArray(arr, n) :`   `    ``# find sum of all prime number` `    ``sum` `=` `0` `    ``for` `i ``in` `range``(n) :`   `        ``if` `prime[arr[i]] :` `            ``sum` `+``=` `arr[i]`   `    ``# if sum is prime` `    ``# then return yes` `    ``if` `prime[``sum``] :` `        ``return` `True`   `    ``return` `False`   `# Driver code` `if` `__name__ ``=``=` `"__main__"` `:`   `    ``# list of elements` `    ``arr ``=` `[``1``, ``2``, ``3``]` `    ``n ``=` `len``(arr)`   `    ``sieve()`   `    ``if` `checkArray(arr, n) :` `        ``print``(``"Yes"``)` `    ``else` `:` `        ``print``(``"No"``)` `        `  `# This code is contributed by ANKITRAI1`

## C#

 `// C# implementation of the above approach` `using` `System;`   `class` `GFG` `{` `static` `int` `MAX = 100000;`   `static` `bool``[] prime = ``new` `bool``[MAX];`   `// Sieve to find prime` `static` `void` `sieve()` `{` `    ``for``(``int` `i = 0; i < MAX; i++)` `    ``{` `        ``prime[i] = ``true``;` `    ``}` `    ``prime[0] = prime[1] = ``false``;` `    ``for` `(``int` `i = 2; i < MAX; i++) ` `        ``if` `(prime[i]) ` `            ``for` `(``int` `j = 2 * i; ` `                     ``j < MAX; j += i)` `                ``prime[j] = ``false``;` `}`   `// Function to check if the sum of` `// prime is prime or not` `static` `bool` `checkArray(``int``[] arr, ``int` `n)` `{` `    ``// find sum of all prime number` `    ``int` `sum = 0;` `    ``for` `(``int` `i = 0; i < n; i++)` `        ``if` `(prime[arr[i]])` `            ``sum += arr[i];`   `    ``// if sum is prime` `    ``// then return yes` `    ``if` `(prime[sum])` `        ``return` `true``;`   `    ``return` `false``;` `}`   `// Driver code` `public` `static` `void` `Main ()` `{` `    ``// array of elements` `    ``int``[] arr = ``new` `int``[] { 1, 2, 3 };` `    ``int` `n = arr.Length;` `    `  `    ``sieve();` `    `  `    ``if` `(checkArray(arr, n))` `        ``Console.WriteLine(``"Yes"``);` `    ``else` `        ``Console.WriteLine(``"No"``);` `}` `}`   `// This code is contributed by mits`

## PHP

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## Javascript

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Output

`Yes`

Complexity Analysis:

• Time Complexity: O(n * log(log n))
• Auxiliary Space: O(MAX)

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