I know there are few that appreciate numbers as much as me. If you're not one of them, stop reading now.
Wikipedia is loaded with information on numbers. I have been focusing lately on prime numbers. Wikipedia lists 59 different "kinds" of prime numbers. A prime fits into a specific category if it is prime and has some other special characteristic.
For example, a prime (i) is a twin prime if (i-2) or (i+2) is also prime. That is, 5 and 7 are twin primes, but 13 and 17 are not.
Another interesting class of primes is "Illegal Primes". Illegal primes are numbers that are prime and also illegal. The web quotes only two numbers to be potentially illegal primes. The numbers could be considered illegal because their binary representation could be deemed illegal.
The example of this is the DVD decrypting program DeCSS. That is, the DeCSS application could be archived (merely to allow for padding, I guess). It's binary code could then be converted to the decimal equivalent of a prime number, thus making the decimal number illegal. (by decimal i mean base-10, not a number with a decimal point.)