#include <iostream>
#include <list>

// Disclaimer. I read the Sieve of Eratosthenes wikipedia article.

int main() {
	std::list<unsigned int> prime_list(1, 2);
	std::list<unsigned int>::iterator prime_iter;
	unsigned int n;
	unsigned int list_num = 0;
	std::list<unsigned int> number_list;
	std::list<unsigned int>::iterator number_iter;
	while(true) {
		n = list_num * 100000 + 2;
		number_list.clear();
		// Build the next 100k numbers.
		while(n < (list_num + 1) * 100000 + 2) {
			number_list.push_back(n);
			++n;
		}

		// Sieve with what we already have.
		for(prime_iter = prime_list.begin(); prime_iter != prime_list.end(); ++prime_iter) {
			if(*prime_iter * *prime_iter > number_list.back()) break;
			number_iter = number_list.begin();
			while(number_iter != number_list.end()) {
				if(*number_iter % *prime_iter == 0) {
					number_iter = number_list.erase(number_iter);
				}
				else {
					++number_iter;
				}
			}
		}

		while(prime_list.back() * prime_list.back() < number_list.back()) {
			prime_list.push_back(number_list.front());
			number_list.pop_front();

			// Sieve using the new prime.
			number_iter = number_list.begin();
			while(number_iter != number_list.end()) {
				if(*number_iter % prime_list.back() == 0) {
					number_iter = number_list.erase(number_iter);
				}
				else {
					++number_iter;
				}
			}
		}
		// The rest of the numbers are primes as well.
		prime_list.splice(prime_list.end(), number_list);

		if(prime_list.size() > 10000) {
			prime_iter = prime_list.begin();
			n = 1;
			while(n != 10001) {
				++prime_iter;
				++n;
			}
			std::cout << *prime_iter << std::endl;
			return 0;
		}

		++list_num;
	}
}

Timeout