vector<int> sieveOfEratosthenes(int n) {
    vector<bool> isPrime(n + 1, true);
    isPrime[0] = isPrime[1] = false; // 0 and 1 are not prime numbers

    for (int i = 2; i * i <= n; i++) {
        if (isPrime[i]) {
            for (int j = i * i; j <= n; j += i) {
                isPrime[j] = false;
            }
        }
    }

    std::vector<int> primes;
    for (int i = 2; i <= n; i++) {
        if (isPrime[i]) {
            primes.push_back(i);
        }
    }

    return primes;
}