What is the 10001st prime number?

10001st Prime.cpp

#include <bits/stdc++.h>
#include <cassert>
using namespace std;

int main() {
    int n = 10001;
    int limit = n/2;
    vector<int> prime;

    while (true) {
        limit *= 2;
        prime.resize(limit + 1, 1);
        for (int i = 2; i * i <= limit; i++) {
            if (prime[i]) {
                for (int k = i * i; k <= limit; k += i) {
                    prime[k] = 0;
                }
            }
        }
        int lastPrime = 1;
        int count = 0;
        for (int i = 2; i <= limit; i++) {
            if (prime[i]) {
                count++;
                lastPrime = i;
            }
            if (count == n) {
                break;
            }
        }
        if (count == n) {
            cout << lastPrime << '\n';
            break;
        }
    }
}