Re: DDMMYY-XXXX
No, it is lower than that. Last digit is for a check digit***) and is odd for males and even for females*) and the first X indicates century **). The system was designed in the late 60es when memory was precious, the population about 4.5 million (now 5.4). With that population, you need in average about 200 numbers per date where you have 540 according to Wikipedia: https://da.wikipedia.org/wiki/CPR-nummer
The nice thing about it is that as resident you only ever have to remember one number, and a 4-digit one in reality.
The Really Scary thing about it is how much can be found about about you with very little effort as _everything_ has it: Banks, tax, libraries, employment contracts, passports. DB people like it as it is guaranteed unique.
If you try to fake one you are likely to be found out pretty quickly, banks typically get your address from the public register.
*) Yes, this has given controversy regarding sex change, trans, and what have you.
**) It has happened that developers forgot to do a check here and asked the 105 year old to come with parents to register for school.
***) I just found this seems to have been abolished in 2007.