Added Linear Sieve Algorithm

Algorithms/Numeric/LinearSieveOfEratosthenes.cs

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+using System;
+using System.Collections.Generic;
+using System.Diagnostics; 
+using System.Linq;
+
+/***
+* Generates all prime numbers up to a given number
+* Wikipedia: http://e-maxx.ru/algo/prime_sieve_linear
+*/
+
+
+namespace Algorithms.Numeric
+{
+    public static class LinearSieveOfEratosthenes
+    {
+        /// <summary>
+        /// Calculate primes up to a given number
+        /// Time Complexity: O(N)
+        /// Memory: O(N)
+        /// </summary>
+        public static List<int> GeneratePrimesUpTo(int N)
+        {
+            //if N is negative, we should return empty list of primes
+            if (N < 0) return new List<int>();
+
+
+            int[] lp=new int[N+1];
+
+            //List of primes
+            var pr = new List<int>();
+
+            int op = 0;
+            for (int i = 2; i <= N; ++i)
+            {
+                if (lp[i] == 0)
+                {
+                    lp[i] = i;
+                    pr.Add(i);
+                }
+                for (int j = 0; j < pr.Count && pr[j] <= lp[i] && i * pr[j] <= N; ++j)
+                {
+                    lp[i * pr[j]] = pr[j];
+                    op++;
+                }
+            } 
+
+            return pr;
+        }
+
+    }
+}

UnitTest/AlgorithmsTests/LinearSieveOfEratosthenesTests.cs

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+using Algorithms.Numeric;
+using System.Linq;
+using Xunit;
+using Xunit.Abstractions;
+
+using System.Diagnostics;
+namespace UnitTest.AlgorithmsTests
+{
+    public class LinearSieveOfEratosthenesTests
+    {
+        private readonly ITestOutputHelper _testOutputHelper;
+        public LinearSieveOfEratosthenesTests(ITestOutputHelper testOutputHelper)
+        {
+            _testOutputHelper = testOutputHelper;
+        }
+        private const int MaxNumber = 100;
+
+        [Fact]
+        public void DoTests()
+        {
+            var results = LinearSieveOfEratosthenes.GeneratePrimesUpTo(MaxNumber);
+            Assert.NotNull(results);
+            Assert.True(results.Any());
+            Assert.Equal(results.Count(), 25);
+            Assert.DoesNotContain(1, results);
+            Assert.Contains(2, results);
+            Assert.Contains(7, results);
+            Assert.Contains(23, results);
+            Assert.Contains(41, results);
+            Assert.Contains(97, results);
+
+        }
+
+        [Fact]
+        public void TestsForEmpty()
+        {
+            var results = LinearSieveOfEratosthenes.GeneratePrimesUpTo(0);
+            Assert.NotNull(results);
+            Assert.False(results.Any());
+
+            var results2 = LinearSieveOfEratosthenes.GeneratePrimesUpTo(-100);
+            Assert.NotNull(results2);
+            Assert.False(results2.Any());
+        }
+    }
+}