Sum of all prime numbers

#include<iostream>
#include<cmath>
//#define max_index 1000001
//  The code doesn't run for above value of Max_index
//  But is accepted in Geeks For Geeks
#define max_index 100000
//  But Runs fine for this value
using namespace std;

int main(){
    long long int prime[max_index], i, j;
    prime[0] = 0;
    for(i = 1; i < max_index; i++){
        prime[i] = i;
    }
    for(i = 2; i < max_index; i++){
        for(j = i + i; j < max_index; j += i){
            if(prime[j] % i == 0) prime[j] = 0;
        }
    }
    //  Showing the list of Prime numbers
    /*
    for(i = 1; i < max_index; i++){
        if(prime[i] != 0) cout << prime[i] << ' ';
    }
    cout << endl;
    */

    int t; cin >> t;
    while(t--){
        int n; cin >> n;
        int result = 0, k = 2;
        while(prime[k] <= n){
            result += prime[k++];
        }
        cout << result << endl;
    }
}