CPR number contains Age and Sex. It's date of birt DD MM YY. Plus four digits where you can read the sex from. I think it's even vs uneven numbers.
There is some interesting details that may require you to change your name, if you want the last digit changed. That means if you're name is Kurt, you can't have a CPR number ending in an even number, because Kurt is only an approved name for men. If your name is Kim, Storm, Charlie, Orla, Lykke or some other unisex name it's not a problem.
This is most worrying for the Danish. Come to think of it, it's worrying for all o f us.