update python and c# to using (Sieve of Eratosthenes) algorithm

prime.cs

@@ -1,31 +1,82 @@
+// using System;
+
+// class Program{
+//     static bool is_prime(int n) {
+//         if (n <= 1) {
+//             return false;
+//         }
+//         var end = Math.Sqrt(n);
+//         for(int i = 2 ; i <= end ; i++)
+//             if (n % i == 0) {
+//                 return false;
+//             }
+//         return true;
+//     }
+//     static void Main(string[] args){
+//         var start = DateTime.Now;
+//         var c = 0;
+//         for (int i=0;i<9000000;i++){
+//             if (is_prime(i)){
+//                 c++;
+//             }
+//         }
+
+//         var end = DateTime.Now;
+
+//         Console.WriteLine(c);
+//         Console.Write( (int) (end-start).TotalMilliseconds );
+//         Console.WriteLine("ms");
+//     }
+
+// }
+
 using System;
 
-class Program{
-    static bool is_prime(int n) {
-        if (n <= 1) {
-            return false;
+class Program
+{
+    static void Main(string[] args)
+    {
+        var start = DateTime.Now;
+        int N = 9000000;
+        bool[] isPrime = new bool[N + 1];
+
+        // Initialize all numbers to be prime
+        for (int i = 2; i <= N; i++)
+        {
+            isPrime[i] = true;
         }
-        var end = Math.Sqrt(n);
-        for(int i = 2 ; i <= end ; i++)
-            if (n % i == 0) {
-                return false;
+
+        // Mark all multiples of each prime as not prime
+        for (int i = 2; i * i <= N; i++)
+        {
+            if (isPrime[i])
+            {
+                for (int j = i * i; j <= N; j += i)
+                {
+                    isPrime[j] = false;
+                }
             }
-        return true;
-    }
-    static void Main(string[] args){
-        var start = DateTime.Now;
-        var c = 0;
-        for (int i=0;i<9000000;i++){
-            if (is_prime(i)){
+        }
+
+        int c = 0;
+        // Print all prime numbers
+        Console.WriteLine("Prime numbers:");
+        for (int i = 2; i <= N; i++)
+        {
+            if (isPrime[i])
+            {
                 c++;
             }
+
         }
 
-        var end = DateTime.Now;
+        var end = (DateTime.Now - start).TotalMilliseconds;
+
 
         Console.WriteLine(c);
-        Console.Write( (int) (end-start).TotalMilliseconds );
-        Console.WriteLine("ms");
-    }
+        Console.WriteLine(String.Format("{0} in {1} ms", c,end));
 
+        Console.ReadKey();
+    }
 }
+

prime.py

@@ -1,22 +1,40 @@
-import math
-import time
+# general way for this problem
+# import math
+# import time
 
-def is_prime(n):
-    if n <= 1:
-        return False;
+# def is_prime(n):
+#     if n <= 1:
+#         return False;
 
-    end = int(math.sqrt(n))
-    for i in range(2, end+1):
-        if n % i == 0:
-            return False
-    return True
+#     end = int(math.sqrt(n))
+#     for i in range(2, end+1):
+#         if n % i == 0:
+#             return False
+#     return True
+
+
+# start = time.time() * 1000
+# c = 0
+# for i in range(0,9000000):
+#     if is_prime(i):
+#         c+=1
 
+# print(c);
+# print( (time.time()*1000) - start);
 
-start = time.time() * 1000
-c = 0
-for i in range(0,9000000):
-    if is_prime(i):
-        c+=1
 
-print(c);
-print( (time.time()*1000) - start);
+# implementation via (Sieve of Eratosthenes) algorithm
+import time
+
+def count_primes(n: int) -> int:
+    s = time.time() * 1000
+    primes = [True] * n
+    primes[0] = primes[1] = False
+    for i in range(2, int(n ** 0.5) + 1):
+        if primes[i]:
+            for j in range(i * i, n, i):
+                primes[j] = False
+    return sum(primes), (time.time() * 1000 - s)
+
+c,e = count_primes(9000000)
+print(f"Found {c} prime number in {e}ms")