C#

List<Number> numbers = new List<Number>() { 2, 3, 4, 5, 6, ... , 2000000 };

for (int i = 0; i < numbers.Count - 1; i++)
   if (numbers[i].IsPrime)
      for (int j = i + 1; j < numbers.Count - 1; j++)
              if (numbers[j].Value % numbers[i].Value == 0)
                     numbers[j].IsPrime = false;

List<Number> numbers = new List<Number>() { 2, 3, 4, 5, 6, ... , 2000000 };

Meysam Tolouee wrote:

It Compiles.

for i = 2, 3, 4, ..., √n :
  if A[i] is true:
    for j = i2, i2+i, i2+2i, ..., n:
      A[j] := false

//1. Create a list of consecutive integers from 2 to n: (2, 3, 4, ..., n).
List<int> numbers = new List<int>();
for (int i = 2; i < 2000000; i++)
    numbers.Add(i);

//2. Initially, let p equal 2, the first prime number.
for (int p = 0; p < numbers.Count - 1; p++)
   if (numbers[p].IsPrime)
      for (int j = p + 1; j < numbers.Count - 1; j++)
          //note that some of them may have already been marked.
          if (numbers[p].IsPrime)
          //3. Starting from p, count up in increments of p and mark each of these numbers greater than p itself in the list. These numbers will be 2p, 3p, 4p, etc
              if (numbers[j].Value % numbers[p].Value == 0)
                  numbers[j].IsPrime = false;

Meysam Tolouee wrote:

for (int p = 0; p < numbers.Count - 1; p++)

Meysam Tolouee wrote:

if (numbers[j].Value % numbers[p].Value == 0)

static void Brute(int max)
{
    var numbers = new List<Number>();
    for (int i = 2; i < max; i++)
        numbers.Add(new Number(i));

    var sw = new Stopwatch();
    sw.Start();
    for (int i = 0; i < numbers.Count - 1; i++)
        if (numbers[i].IsPrime)
            for (int j = i + 1; j < numbers.Count - 1; j++)
                if (numbers[j].Value % numbers[i].Value == 0)
                    numbers[j].IsPrime = false;

    sw.Stop();
    Console.WriteLine("Brute: {0}ms",sw.ElapsedMilliseconds);
}

Brute: 152009ms

Sieve:15ms

Meysam Tolouee wrote:

nd you are not going to help me.

private static bool[] _numbers;

static void Main(string[] args)
{
    var sw = new Stopwatch();
    sw.Start();
    Run();
    sw.Stop();
    Console.WriteLine("Milliseconds run: " + sw.ElapsedMilliseconds);
    Console.WriteLine("Primes: " + _numbers.Count(i => i));
    Console.ReadLine();
}

private static void Run()
{
    const int count = 2000000;
    _numbers = new bool[count];
    for (int i = 2; i < count; i++)
        _numbers[i] = true;

    int baseCounter = 1;

    while (baseCounter < count)
    {
        do
        {
            baseCounter++;
            if (baseCounter == count) return;
        } while (!_numbers[baseCounter]);

        int counter = baseCounter << 1;
        while (counter < count)
        {
            _numbers[counter] = false;
            counter += baseCounter;
        }
    }

long sum = 0;
for (int i = 0; i < _numbers.Length - 1; i++)
{
   if (_numbers[i])
      sum += i;
}

static void Main(string[] args)
    {
        var sw = new Stopwatch();
        sw.Start();
        Run();
        sw.Stop();
        Console.WriteLine("Milliseconds run: " + sw.ElapsedMilliseconds);
        Console.WriteLine("Primes: " + _numbers.Count(i => i));
        var sum = 0;
        for (int i = 2; i < _numbers.Count(); i++)
            if (_numbers[i]) sum += i;
        Console.WriteLine("Sum of Primes: " + sum.ToString("n0"));

        Console.ReadLine();
    }