diff --git a/math/prime_numbers.cpp b/math/prime_numbers.cpp
index 4dd54f136..cd6aca0ca 100644
--- a/math/prime_numbers.cpp
+++ b/math/prime_numbers.cpp
@@ -9,14 +9,22 @@
 /** Generate an increasingly large number of primes
  * and store in a list
  */
-std::vector<int> primes(int max) {
-    max++;
+std::vector<int> primes(size_t max) {
     std::vector<int> res;
-    std::vector<bool> numbers(max, false);
-    for (int i = 2; i < max; i++) {
-        if (!numbers[i]) {
-            for (int j = i; j < max; j += i) numbers[j] = true;
-            res.push_back(i);
+    std::vector<bool> is_not_prime(max + 1, false);
+    for (size_t i = 2; i <= max; i++) {
+        if (!is_not_prime[i]) {
+            res.emplace_back(i);
+        }
+        for (int p : res) {
+            size_t k = i * p;
+            if (k > max) {
+                break;
+            }
+            is_not_prime[k] = true;
+            if (i % p == 0) {
+                break;
+            }
         }
     }
     return res;
@@ -25,9 +33,9 @@ std::vector<int> primes(int max) {
 /** main function */
 int main() {
     std::cout << "Calculate primes up to:\n>> ";
-    int n;
+    int n = 0;
     std::cin >> n;
     std::vector<int> ans = primes(n);
-    for (int i = 0; i < ans.size(); i++) std::cout << ans[i] << ' ';
+    for (int p : ans) std::cout << p << ' ';
     std::cout << std::endl;
 }