# 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 **K ^{th}** array.

**Examples:**

Input:K = 3Output:31

arr1[] = {2}

arr[] = {3, 5}

arr[] = {7, 11, 13}

7 + 11 + 13 = 31Input:K = 2Output:8

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**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++

`// C++ implementation of the approach` `#include <bits/stdc++.h>` `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

`// 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<Integer> 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

`# 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#

`// 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` |

## Javascript

`<script>` `// Javascript implementation of the approach\` `const MAX = 1000000;` `// To store whether a number is prime or not` `let prime = ` `new` `Array(MAX);` `// Function for Sieve of Eratosthenes` `function` `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` `(let i = 0; i < MAX; i++)` ` ` `prime[i] = ` `true` `;` ` ` `for` `(let 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` `(let i = p * p; i < MAX; i += p)` ` ` `prime[i] = ` `false` `;` ` ` `}` ` ` `}` `}` `// Function to return the sum of` `// primes in the Kth array` `function` `sumPrime(k)` `{` ` ` `// Update vector v to store all the` ` ` `// prime numbers upto MAX` ` ` `SieveOfEratosthenes();` ` ` `let v = [];` ` ` `for` `(let i = 2; i < MAX; i++) {` ` ` `if` `(prime[i])` ` ` `v.push(i);` ` ` `}` ` ` `// To store the sum of primes` ` ` `// in the kth array` ` ` `let sum = 0;` ` ` `// Count of primes which are in` ` ` `// the arrays from 1 to k - 1` ` ` `let skip = parseInt((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` ` ` `let k = 3;` ` ` `document.write(sumPrime(k));` `</script>` |

**Output:**

31