HashSet

using System;
using System.Collections.Generic;

public static class Sieve
{
    public static IEnumerable<int> Primes(int max)
    {
        if (max < 0)
            throw new ArgumentOutOfRangeException(nameof(max));

        var primeMultiples = new HashSet<int>();

        for (var i = 2; i <= max; i++)
        {
            if (primeMultiples.Contains(i))
                continue;

            for (var j = i * 2; j <= max; j += i)
                primeMultiples.Add(j);

            yield return i;
        }
    }
}

The first step is to check the input for validity:

if (max < 0)
    throw new ArgumentOutOfRangeException(nameof(max));

We then create a HashSet<int> that will contain the numbers that are a multiple of the primes we find:

var primeMultiples = new HashSet<int>();

We then start iterating from 2 (the smallest prime) up until the maximum that was specified:

for (var i = 2; i <= max; i++)

Within the loop, our first check is to see if the current number (i) is a multiple of one of the primes we found. If so, we'll skip the number as it can't be a prime:

if (primeMultiples.Contains(i))
    continue;

If this check returns false, we're dealing with a prime! This means that we can then cross off any multiples of this prime, which we can do with another (nested) for-loop:

for (var j = i * 2; j <= max; j += i)
    primeMultiples.Add(j);

Note how we start at the first multiple of the prime (i * 2) and that we increment the loop iterator variable by the prime number (j += i) to iterate over all the multiples of the prime.

The final step is to return the prime number, for which we use a yield statement:

yield return i;

Note that even though we yield an indidivual integer, what is returned from a caller's viewpoint is a sequence of integers.