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

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 print Yes otherwise No.

Below is the implementation of the above approach:

C++

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// C++ implementation of the above approach
#include <bits/stdc++.h>
#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;
}

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Java














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// 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<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 boolean 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 (String[] args) { 


    // array of elements 


    int arr[] = { 1, 2, 3 }; 


    int n = arr.length; 


  


    sieve(); 


  


    if (checkArray(arr, n)) 


        System.out.println("Yes"); 


    else


         System.out.println("No"); 


  


    } 


} 


// This code is contributed by shs.. 



















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Python3














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# 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 



















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C#














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// 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 



















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PHP














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<?php 


// PHP implementation of the  


// above approach 


  


// Sieve to find prime 


function sieve() 


{ 


    $MAX = 100000; 


    $prime = array($MAX); 


    for($i = 0; $i < $MAX; $i++) 


    { 


        $prime[$i] = true; 


    } 


    $prime[0] = $prime[1] = false; 


    for ($i = 2; $i < $MAX; $i++)  


        if ($prime[$i])  


            for ($j = 2 * $i;  


                 $j < $MAX; $j += $i) 


                $prime[$j] = false; 


} 


  


// Function to check if the sum of 


// prime is prime or not 


function checkArray($arr, $n) 


{ 


    $prime = array(100000); 


      


    // find sum of all prime number 


    $sum = 0; 


    for ($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 


$arr= array(1, 2, 3); 


$n = sizeof($arr); 


  


sieve(); 


  


if (checkArray($arr, $n)) 


    echo "Yes"; 


else


    echo "No"; 


  


// This code is contributed 


// by Akanksha Rai 


?> 



















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Output:


Yes







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