# Find the sum of prime numbers in the Kth array

Given K arrays where the first array contains the first prime number, the second array contains the next 2 primes and the third array contains the next 3 primes and so on. The task is to find the sum of primes in the Kth array.

Examples:

Input: K = 3
Output: 31
arr1[] = {2}
arr[] = {3, 5}
arr[] = {7, 11, 13}
7 + 11 + 13 = 31

Input: K = 2
Output: 8

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

Approach: Sieve of Eratosthenes can be used to find all the prime upto the required element. And the count of prime numbers in the arrays from 1 to K – 1 will be cnt = 1 + 2 + 3 + … + (K – 1) = (K * (K – 1)) / 2. Now, starting from the (cnt + 1)th prime from the sieve array, start adding all the primes until exactly K primes are added then print the sum.

Below is the implementation of the above approach:

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` `#define MAX 1000000 ` ` `  `// To store whether a number is prime or not ` `bool` `prime[MAX]; ` ` `  `// Function for Sieve of Eratosthenes ` `void` `SieveOfEratosthenes() ` `{ ` `    ``// Create a boolean array "prime[0..n]" and initialize ` `    ``// all entries it as true. A value in prime[i] will ` `    ``// finally be false if i is Not a prime, else true. ` `    ``for` `(``int` `i = 0; i < MAX; i++) ` `        ``prime[i] = ``true``; ` ` `  `    ``for` `(``int` `p = 2; p * p < MAX; p++) { ` ` `  `        ``// If prime[p] is not changed then it is a prime ` `        ``if` `(prime[p]) { ` ` `  `            ``// Update all multiples of p greater than or ` `            ``// equal to the square of it ` `            ``// numbers which are multiple of p and are ` `            ``// less than p^2 are already been marked. ` `            ``for` `(``int` `i = p * p; i < MAX; i += p) ` `                ``prime[i] = ``false``; ` `        ``} ` `    ``} ` `} ` ` `  `// Function to return the sum of ` `// primes in the Kth array ` `int` `sumPrime(``int` `k) ` `{ ` ` `  `    ``// Update vector v to store all the ` `    ``// prime numbers upto MAX ` `    ``SieveOfEratosthenes(); ` `    ``vector<``int``> v; ` `    ``for` `(``int` `i = 2; i < MAX; i++) { ` `        ``if` `(prime[i]) ` `            ``v.push_back(i); ` `    ``} ` ` `  `    ``// To store the sum of primes ` `    ``// in the kth array ` `    ``int` `sum = 0; ` ` `  `    ``// Count of primes which are in ` `    ``// the arrays from 1 to k - 1 ` `    ``int` `skip = (k * (k - 1)) / 2; ` ` `  `    ``// k is the number of primes ` `    ``// in the kth array ` `    ``while` `(k > 0) { ` `        ``sum += v[skip]; ` `        ``skip++; ` ` `  `        ``// A prime has been ` `        ``// added to the sum ` `        ``k--; ` `    ``} ` ` `  `    ``return` `sum; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `k = 3; ` ` `  `    ``cout << sumPrime(k); ` ` `  `    ``return` `0; ` `} `

 `// Java implementation of the approach ` `import` `java.util.*; ` ` `  `class` `GFG  ` `{ ` ` `  `static` `int` `MAX = ``1000000``; ` ` `  `// To store whether a number is prime or not ` `static` `boolean` `[]prime = ``new` `boolean``[MAX]; ` ` `  `// Function for Sieve of Eratosthenes ` `static` `void` `SieveOfEratosthenes() ` `{ ` `    ``// Create a boolean array "prime[0..n]" and  ` `    ``// initialize all entries it as true.  ` `    ``// A value in prime[i] will finally be false ` `    ``// if i is Not a prime, else true. ` `    ``for` `(``int` `i = ``0``; i < MAX; i++) ` `        ``prime[i] = ``true``; ` ` `  `    ``for` `(``int` `p = ``2``; p * p < MAX; p++)  ` `    ``{ ` ` `  `        ``// If prime[p] is not changed ` `        ``// then it is a prime ` `        ``if` `(prime[p])  ` `        ``{ ` ` `  `            ``// Update all multiples of p greater than or ` `            ``// equal to the square of it ` `            ``// numbers which are multiple of p and are ` `            ``// less than p^2 are already been marked. ` `            ``for` `(``int` `i = p * p; i < MAX; i += p) ` `                ``prime[i] = ``false``; ` `        ``} ` `    ``} ` `} ` ` `  `// Function to return the sum of ` `// primes in the Kth array ` `static` `int` `sumPrime(``int` `k) ` `{ ` ` `  `    ``// Update vector v to store all the ` `    ``// prime numbers upto MAX ` `    ``SieveOfEratosthenes(); ` `    ``Vector v = ``new` `Vector<>(); ` `    ``for` `(``int` `i = ``2``; i < MAX; i++)  ` `    ``{ ` `        ``if` `(prime[i]) ` `            ``v.add(i); ` `    ``} ` ` `  `    ``// To store the sum of primes ` `    ``// in the kth array ` `    ``int` `sum = ``0``; ` ` `  `    ``// Count of primes which are in ` `    ``// the arrays from 1 to k - 1 ` `    ``int` `skip = (k * (k - ``1``)) / ``2``; ` ` `  `    ``// k is the number of primes ` `    ``// in the kth array ` `    ``while` `(k > ``0``) ` `    ``{ ` `        ``sum += v.get(skip); ` `        ``skip++; ` ` `  `        ``// A prime has been ` `        ``// added to the sum ` `        ``k--; ` `    ``} ` ` `  `    ``return` `sum; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `k = ``3``; ` ` `  `    ``System.out.println(sumPrime(k)); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

 `# Python3 implementation of the approach  ` `from` `math ``import` `sqrt ` ` `  `MAX` `=` `1000000` ` `  `# Create a boolean array "prime[0..n]" and  ` `# initialize all entries it as true.  ` `# A value in prime[i] will finally be false  ` `# if i is Not a prime, else true.  ` `prime ``=` `[``True``] ``*` `MAX` ` `  `# Function for Sieve of Eratosthenes  ` `def` `SieveOfEratosthenes() : ` ` `  `    ``for` `p ``in` `range``(``2``, ``int``(sqrt(``MAX``)) ``+` `1``) :  ` ` `  `        ``# If prime[p] is not changed ` `        ``# then it is a prime  ` `        ``if` `(prime[p]) : ` ` `  `            ``# Update all multiples of p greater than or  ` `            ``# equal to the square of it  ` `            ``# numbers which are multiple of p and are  ` `            ``# less than p^2 are already been marked.  ` `            ``for` `i ``in` `range``(p ``*` `p, ``MAX``, p) : ` `                ``prime[i] ``=` `False``;  ` ` `  `# Function to return the sum of  ` `# primes in the Kth array  ` `def` `sumPrime(k) :  ` ` `  `    ``# Update vector v to store all the  ` `    ``# prime numbers upto MAX  ` `    ``SieveOfEratosthenes();  ` `    ``v ``=` `[];  ` `    ``for` `i ``in` `range``(``2``, ``MAX``) : ` `        ``if` `(prime[i]) : ` `            ``v.append(i);  ` ` `  `    ``# To store the sum of primes  ` `    ``# in the kth array  ` `    ``sum` `=` `0``;  ` ` `  `    ``# Count of primes which are in  ` `    ``# the arrays from 1 to k - 1  ` `    ``skip ``=` `(k ``*` `(k ``-` `1``)) ``/``/` `2``;  ` ` `  `    ``# k is the number of primes  ` `    ``# in the kth array  ` `    ``while` `(k > ``0``) : ` `        ``sum` `+``=` `v[skip];  ` `        ``skip ``+``=` `1``;  ` ` `  `        ``# A prime has been  ` `        ``# added to the sum  ` `        ``k ``-``=` `1``;  ` ` `  `    ``return` `sum``;  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `: ` `     `  `    ``k ``=` `3``; ` `     `  `    ``print``(sumPrime(k));  ` ` `  `# This code is contributed by AnkitRai01 `

 `// C# mplementation of the approach ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG  ` `{ ` `static` `int` `MAX = 1000000; ` ` `  `// To store whether a number is prime or not ` `static` `bool` `[]prime = ``new` `bool``[MAX]; ` ` `  `// Function for Sieve of Eratosthenes ` `static` `void` `SieveOfEratosthenes() ` `{ ` `    ``// Create a boolean array "prime[0..n]" and  ` `    ``// initialize all entries it as true.  ` `    ``// A value in prime[i] will finally be false ` `    ``// if i is Not a prime, else true. ` `    ``for` `(``int` `i = 0; i < MAX; i++) ` `        ``prime[i] = ``true``; ` ` `  `    ``for` `(``int` `p = 2; p * p < MAX; p++)  ` `    ``{ ` ` `  `        ``// If prime[p] is not changed ` `        ``// then it is a prime ` `        ``if` `(prime[p])  ` `        ``{ ` ` `  `            ``// Update all multiples of p greater than or ` `            ``// equal to the square of it ` `            ``// numbers which are multiple of p and are ` `            ``// less than p^2 are already been marked. ` `            ``for` `(``int` `i = p * p; i < MAX; i += p) ` `                ``prime[i] = ``false``; ` `        ``} ` `    ``} ` `} ` ` `  `// Function to return the sum of ` `// primes in the Kth array ` `static` `int` `sumPrime(``int` `k) ` `{ ` ` `  `    ``// Update vector v to store all the ` `    ``// prime numbers upto MAX ` `    ``SieveOfEratosthenes(); ` `    ``List<``int``> v = ``new` `List<``int``>(); ` `    ``for` `(``int` `i = 2; i < MAX; i++)  ` `    ``{ ` `        ``if` `(prime[i]) ` `            ``v.Add(i); ` `    ``} ` ` `  `    ``// To store the sum of primes ` `    ``// in the kth array ` `    ``int` `sum = 0; ` ` `  `    ``// Count of primes which are in ` `    ``// the arrays from 1 to k - 1 ` `    ``int` `skip = (k * (k - 1)) / 2; ` ` `  `    ``// k is the number of primes ` `    ``// in the kth array ` `    ``while` `(k > 0) ` `    ``{ ` `        ``sum += v[skip]; ` `        ``skip++; ` ` `  `        ``// A prime has been ` `        ``// added to the sum ` `        ``k--; ` `    ``} ` ` `  `    ``return` `sum; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `k = 3; ` ` `  `    ``Console.WriteLine(sumPrime(k)); ` `} ` `} ` ` `  `// This code is contributed by PrinciRaj1992 `

Output:
```31
```

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 :