// Miller-Rabin primality test as an extension method on the BigInteger type.
// Based on the Ruby implementation on this page.
public static class BigIntegerExtensions
{
  public static bool IsProbablePrime(this BigInteger source, int certainty)
  {
    if(source == 2 || source == 3)
      return true;
    if(source < 2 || source % 2 == 0)
      return false;

    BigInteger d = source - 1;
    int s = 0;

    while(d % 2 == 0)
    {
      d /= 2;
      s += 1;
    }

    // There is no built-in method for generating random BigInteger values.
    // Instead, random BigIntegers are constructed from randomly generated
    // byte arrays of the same length as the source.
    RandomNumberGenerator rng = RandomNumberGenerator.Create();
    byte[] bytes = new byte[source.ToByteArray().LongLength];
    BigInteger a;

    for(int i = 0; i < certainty; i++)
    {
      do
      {
        // This may raise an exception in Mono 2.10.8 and earlier.
        // http://bugzilla.xamarin.com/show_bug.cgi?id=2761
        rng.GetBytes(bytes);
        a = new BigInteger(bytes);
      }
      while(a < 2 || a >= source - 2);

      BigInteger x = BigInteger.ModPow(a, d, source);
      if(x == 1 || x == source - 1)
        continue;

      for(int r = 1; r < s; r++)
      {
        x = BigInteger.ModPow(x, 2, source);
        if(x == 1)
          return false;
        if(x == source - 1)
          break;
      }

      if(x != source - 1)
        return false;
    }

    return true;
  }
}