We, in Romania, do not understand how is calculated the special mathematical number 279146358279 , which is prezent in calculation of CNP (personal identification number) received by all citizen from romanian authorities.
This number refers to Modulo 11.
This number is described for Romania also in Wikipeda. Please lookdown (search) for Romania: https://en.m.wikipedia.org/wiki/National_identification_number
Thank You! Ioan Rudu
This is a fairly standard way of making sure a number "makes sense" and is not gibberish. You might look up on Google IBAN codes, used in banking: https://en.wikipedia.org/wiki/International_Bank_Account_Number
The basic idea is to add some digits that come from some 'scrambling' of the original digits in such a way that you can determine with a high probability if the number is valid without requiring looking it up.
As a really simple example, suppose it were like the U.S. and everyone has an 9 digit number, which we write like this: 050-27-1234. One way to do this would be to add up all the digits, take the last digit in the result, and add that to the end. In this case,
$$0+5+0+2+7+1+2+3+4= 23 $$
So the "check" digit is 3 (we drop the '2' from 23), and we now say the number is 050-27-1234-3.
Now you can see it is easy to check if a number is valid by looking at it. For example, if someone mis-wrote it as 060-27-1234-3, we know right away it is an error since the number doesn't 'check' properly.
The approach used in your country is a bit more complex; this is a simple 'sum of the digits modulo 10' checksum. But it wouldn't catch some errors that might easily cancel each other out. For example 050-27-1235-3 checks out OK, but this might indicate two different numbers were written wrong. The whole thing of "multiply each digit by a digit in the magin number and divide modulo 11" just makes it harder for simple little errors to offset each other, and makes the checksum more effective.
Why it works and how these get built is covered in a field (in engineering) called "error-correcting codes" you could Google if you want an explanation, but the actual math gets pretty complex.