title: How can I test for primality?
body: <p>I am writing a little library with some prime number related methods. As I've done the groundwork (aka working methods) and now I'm looking for some optimization. 
  Ofcourse the internet is an excellent place to do so. I've, however, stumbled upon a rounding problem and I was wondering how to solve this.</p>
  
  <p>In the loop I use to test a number for it's primality it's more efficient to search until sqrt(n) instead of n/2 or even n - 1. But due to rounding problems some number get skipped and thus some primes are skipped! For example, the 10000th prime should be: 104729, but the 'optimized' version ends up with: 103811.</p>
  
  <p>Some code (it's open for more optimization, I know, but I can handle only one thing at a time):</p>
  
  <pre><code>/// &lt;summary&gt;
  /// Method for testing the primality of a number e.g.: return IsPrime(29);
  /// History:
  /// 1. Initial version, most basic form of testing: m smaller then n -1
  /// 2. Implemented m smaller then sqrt(n), optimization due to prime factoring
  /// &lt;/summary&gt;
  /// &lt;param name="test"&gt;Number to be tested on primality&lt;/param&gt;
  /// &lt;returns&gt;True if the number is prime, false otherwise&lt;/returns&gt;
  public static bool IsPrime(int test)
  {
      // 0 and 1 are not prime numbers
      if (test == 0 || test == 1) return false;
  
      // 2 and 3 are prime numbers
      if (test == 2) return true;
  
      // all even numbers, save 2, are not prime
      if (test % 2 == 0) return false;
  
      double squared = Math.Sqrt(test);
      int flooredAndSquared = Convert.ToInt32(Math.Floor(squared));
  
      // start with 5, make increments of 2, even numbers do not need to be tested
      for (int idx = 3; idx &lt; flooredAndSquared; idx++)
      {
          if (test % idx == 0)
          {
              return false;
          }
      }
      return true;
  }
  </code></pre>
  
  <p>I know the squared part fails me (or I fail), tried Math.Ceiling as well, with about the same results.</p>