C++ solution O(n/ln(n)) space

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    It seems that all solutions I saw so far used O(n) space. So I came to share my slower (306ms) yet the less space-consuming solution (O(n/ln(n)). See the wiki page prime number theorem for why the space needed is O(n/ln(n)).

    Logic: If a number is not a prime, then it can be divided by at least a prime. Thus, we maintain a vector of primes. Every time a number cannot be divided by the primes we know currently, we add it in.

    class Solution {
        int countPrimes(int n) {
            vector<int> primes;
            for (int i = 2; i < n; ++i) {
                bool isPrime = true;
                int sqrt_i = sqrt(i);
                for (int prime : primes) {
                    if (i % prime == 0) {
                        isPrime = false;
                    } else if (prime > sqrt_i) {
                if (isPrime) {
            return primes.size();

    Any advice to improve the code would be appreciated. Many thanks.

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