How can I test for primality?

I guess this is your problem:

for (int idx = 3; idx < flooredAndSquared; idx++)

This should be

for (int idx = 3; idx <= flooredAndSquared; idx++)

so you don't get square numbers as primes. Also, you can use "idx += 2" instead of "idx++" because you only have to test odd numbers (as you wrote in the comment directly above...).

I posted a class that uses the sieve or Eratosthenes to calculate prime numbers here:

Is the size of an array constrained by the upper limit of int (2147483647)?

I don't know if this is quite what you are looking for but if you are really concerned about speed then you should look into probablistic methods for testing primality rather than using a sieve. Rabin-Miller is a probabilistic primality test used by Mathematica.

Sadly, I haven't tried the algorithmic approaches before. But if you want to implement your approach efficiently, I'd suggest doing some caching. Create an array to store all prime numbers less than a defined threshold, fill this array, and search within/using it.

In the following example, finding whether a number is prime is O(1) in the best case (namely, when the number is less than or equal to maxPrime, which is 821,461 for a 64K buffer), and is somewhat optimized for other cases (by checking mod over only 64K numbers out of the first 820,000 -- about 8%).

(Note: Don't take this answer as the "optimal" approach. It's more of an example on how to optimize your implementation.)

public static class PrimeChecker
{
    private const int BufferSize = 64 * 1024; // 64K * sizeof(int) == 256 KB

    private static int[] primes;
    public static int MaxPrime { get; private set; }

    public static bool IsPrime(int value)
    {
        if (value <= MaxPrime)
        {
            return Array.BinarySearch(primes, value) >= 0;
        }
        else
        {
            return IsPrime(value, primes.Length) && IsLargerPrime(value);
        }
    }

    static PrimeChecker()
    {
        primes = new int[BufferSize];
        primes[0] = 2;
        for (int i = 1, x = 3; i < primes.Length; x += 2)
        {
            if (IsPrime(x, i))
                primes[i++] = x;
        }
        MaxPrime = primes[primes.Length - 1];
    }

    private static bool IsPrime(int value, int primesLength)
    {
        for (int i = 0; i < primesLength; ++i)
        {
            if (value % primes[i] == 0)
                return false;
        }
        return true;
    }

    private static bool IsLargerPrime(int value)
    {
        int max = (int)Math.Sqrt(value);
        for (int i = MaxPrime + 2; i <= max; i += 2)
        {
            if (value % i == 0)
                return false;
        }
        return true;
    }
}