New Development in 2007
The sequence numbers used to be chosen (and still are, preferentially) so that the last digit of the sequence number functions as a check digit for the entire personal identification number. In this case, the number satisfies the equation 4x1 + 3x2 + 2x3 + 7x4 + 6x5 + 5x6 + 4x7 + 3x8 + 2x9 + x10 ≡ 0 (mod 11) where the xi are the ten digits of the complete ID number, and the coefficients (4, 3, 2, 7, …) are all nonzero in the finite field of order 11.
However in 2007 the available sequence numbers under this system for males born on 1 January 1965 ran out, and since October 2007 personal identification numbers do not always validate using the check digit. This had been predicted and announced several years in advance. Thus, most IT systems are presumed updated to accept numbers that fail the check-digit validation.
1 January was the first birth date to run out of sequence numbers because immigrants who do not know their exact date of birth are administratively registered with the fictitious birth date of 1 January. This made the date unusually frequent in the register.
Read more about this topic: Personal Identification Number (Denmark)
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