added SieveOfEratosthenes C# Issue #172

C#/README.md

@@ -3,4 +3,6 @@
 
 [Linked list is palindrome](./linked_list_is_palindrome.cs)
 
+[sieve of eratosthenes](./SieveOfEratosthenes.cs)
+
 [Quick Sort](./quick_sort.cs)

C#/SieveOfEratosthenes.cs

@@ -0,0 +1,69 @@
+using System;
+using System.Collections;
+
+namespace DefaultNamespace
+{
+    public class SieveOfEratosthenes
+    {
+        private static void Main(string[] args)
+        {
+            Console.Write("Please enter a random integer number: ");
+            if (int.TryParse(Console.ReadLine(), out var num))
+            {
+                Console.Write($"All primary numbers between 2 and {num} is : ");
+                GetAllPrimaryNumbers(num);
+            }
+
+            Console.WriteLine();
+        }
+
+        /// <summary>
+        ///     implementing Sieve_of_Eratosthenes
+        /// </summary>
+        /// <param name="num">input</param>
+        /// <returns>list of primary numbers equals or less than input</returns>
+        private static void GetAllPrimaryNumbers(int num)
+        {
+            if (num <= 1) return;
+
+            var cells = new BitArray(num + 1, true);
+            // var cells = new bool[num+1];
+            var p = 2;
+            while (p <= num)
+            {
+                // continue if marked false
+                if (!cells[p])
+                {
+                    p++;
+                    continue;
+                }
+
+                Console.Write(p + ",");
+
+                // mark all multiples of p as false
+                for (var i = p; i < num; i++)
+                {
+                    if (p * i < 2 || p * i > num) break;
+                    cells[p * i] = false;
+                }
+
+                p++;
+            }
+        }
+    }
+}
+
+
+/*
+    // 1
+    Please enter a random number: 10
+    All primary numbers between 2 and 10 is : 2,3,5,7,
+    It took 3957 ms.
+
+    // 2
+    Please enter a random number: 200
+    All primary numbers between 2 and 200 is : 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,
+    83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,
+    It took 1425 ms.
+
+*/