Find Prime Numbers in C# Using the Sieve of Eratosthenes

Hi, Thanks for the feedback for alternative #1 from above (and thank you, Jurgen Rohr for your suggestion! I replaced the "reset" line with:

while (!sieveContainer.Get(++marker));
factor = marker;

Here is another algorithm that's slightly different. It's not as elegant an approach, but appears to run quickly and I thought it was interesting to view the sieving container this way. While testing on my machine comparing alternative #1 from above to this one, I can get both to run about the same, with a slight edge to this new solution for bigger candidate values. Running for candidate = 10^7 ~ 850 milliseconds; 10^8 ~ 10seconds; 10^9 ~ 115 seconds (50 million + primes). Does anyone see ways in which this can be improved? Thanks for your feedback! (and sorry for any typos). Update: Ok, I was able to run this on a pretty ok machine. Here are the results I found.

	Time in Milliseconds
Results	Alt #1	Alt #4	Primes
200,000	6.0	6.0	17,984
2,000,000	54.0	47.0	148,933
20,000,000	550.0	447.0	1,270,607
200,000,000	6955.0	6025.0	11,078,937
2,000,000,000	78,994.0	67,285.0	98,222,287

   //The idea is to narrow the sievingContainer to only look at 1/3 of the numbers. 
        //(knot theory, http://www.scribd.com/doc/9935691/Prime-Numbers-without-Mystery-2
        //Below are 6 columns of numbers. You can see columns 1 (1,7,13,..) and column 5 (5,11,17, ...)
        //Everything in column 2-4,6 can be ignored.
        //Primes are only in columns 1 and 5 (along with prime factors of only 2 primes and primes squared).
        //ie: 25 (5^2), 35 (7*5), 65 (5*13), 49, 91 (7 * 13)
        /*
            1	2	3	4	5	6
            7	8	9	10	11	12
            13	14	15	16	17	18
            19	20	21	22	23	24
            25	26	27	28	29	30
            31	32	33	34	35	36
            37	38	39	40	41	42
            43	44	45	46	47	48
            49	50	51	52	53	54
            55	56	57	58	59	60
            61	62	63	64	65	66
            67	68	69	70	71	72
            73	74	75	76	77	78
            79	80	81	82	83	84
            85	86	87	88	89	90
            91	92	93	94	95	96
            97	98	99	100	101	102
            103	104	105	106	107	108
            ....
        */
        public static int Sieve(int candidate)
        {
            var sieveContainer = new BitArray(candidate + 1, false);

            sieveContainer.Set(2, true);
            sieveContainer.Set(3, true);

            //flag all factors of 6+/-1 as prime. 
            //this initializes our bit array that will be sieved.
            for (int i = 6; i <= candidate; i += 6)
            {
                sieveContainer.Set(i+1, true);
                sieveContainer.Set(i-1, true);
            }


            //Starting at marker (ie: 5), square it and flag that as not prime.
            //Then add marker * 6 to marker starting at marker^2. (ie: 5 * 5 = 25, add 5*6 = 30, so 30+25=55, 85,...). Flag those as not prime
            //Next, add marker * 6 to marker starting at marker. (ie: 5 * 6 + 5 = 35, 65, 95. Flag these as not prime
            //Repeat starting with the next marker not sieved off. ie: 7, 11, 13
            long marker, factor; 
            marker = 5;
            while (marker * 2 <= candidate)
            {
                //sieve the prime^2
                while (marker * marker <= candidate)
                {
                    sieveContainer.Set((int)(marker * marker), false);
                    break;
                }

                //sieve marker plus factors of marker * 6, starting at p^2
                factor = (marker * marker) + (marker * 6);
                while (factor <= candidate)
                {
                    sieveContainer.Set((int)factor, false);
                    factor += marker * 6;
                }

                //sieve marker plus factors of marker * 6
                factor = marker * 6 + marker;
                while (factor <= candidate)
                {
                    sieveContainer.Set((int)factor, false);
                    factor += marker * 6;
                }

                while (!sieveContainer.Get((int)++marker)) ;
            }

            marker = 0;
            int toReturn = 0;
            while (++marker < candidate)
            {
                if (sieveContainer.Get((int)marker))
                    toReturn++;
            }

            return toReturn;
        }
    }