Here is a very very simple eg. of how 'some' serial numbers work.....12342 or 34566. These appear to be random numbers, but i can recognise them as 'my serial numbers' by doing a simple sum.
12342... 1+2+3-4=2 or 34566... 3+4+5-6=6.
If i stick to the same pattern of + + -. I will be able to work out genuine serial numbers from those nasty fakes!!
Now give me a computer and Hexadecimal and 32 bit encryption and all that. I will then be able to generate great long strings of figures.
The trick is though that the computer you have checking the huge 28 or 32 character number 'Knows' the sum +++-+-+= etc.. Or what ever you have previously chosen!