The following method starts by selecting the number 2 and eliminates each multiple of 2 up to N. Then the next valid number is selected and each multiple of it is eliminated. The process is repeated until all valid numbers have been tested. So the first three multiples to be eliminated are those of 2, 3, and 5. The number 4 is skipped as it has already been eliminated because it’s a multiple of 2. A number is eliminated by simply setting the appropriate member of a Boolean array.

static List<int> GetPrimeNumbers(int n)
{
bool[] notPrime = new bool[n + 1];
List<int> primeNumbers = new List<int>();
for (int i = 2; i <= n; i++)
{
if (notPrime[i] == false)
{
int m;
int multiplicand = 2;
while (( m = multiplicand * i) <= n)
{
notPrime[m] = true;
multiplicand++;
}
}
}
for (int i = 2; i <= n; i++)
{
if (notPrime[i] == false)
{
primeNumbers.Add(i);
}
}
return primeNumbers;
}