Danish CPR

What it covers

Returns a valid Danish CPR (Det Centrale Personregister) number. Constrain with `sex` and age/birth-date filters (the full date is encoded). Contradictory combinations are rejected with a 400. Use `checksum` to choose the mod-11 standard, `format` for the rendering, and `invalid=true` for a deliberately wrong check.

How it’s calculated

The Danish CPR number's 10th digit is a weighted mod-11 check digit that makes the whole 10-digit number's weighted sum divisible by 11 (a scheme abandoned for newly-issued numbers since 2007, which this generator can also model).

First nine digits: 0 1 0 1 9 0 4 1 2 (DDMMYY=010190, century/serial digit=4, middle=12).
Weights [4,3,2,7,6,5,4,3,2] applied position by position:
0*4=0, 1*3=3, 0*2=0, 1*7=7, 9*6=54, 0*5=0, 4*4=16, 1*3=3, 2*2=4.
partial = 0+3+0+7+54+0+16+3+4 = 87.
87 mod 11 = 10  (11*7 = 77, 87-77 = 10).
last = (11 - 10) mod 11 = 1 mod 11 = 1. Not 10, so it is valid.
Verify: full weighted sum = 87 + 1*1 = 88 = 11*8, divisible by 11.

Edge cases

• When (11 - (partial mod 11)) mod 11 == 10, no valid check digit exists for that serial; the generator rejects it and redraws the middle serial digits rather than emitting an 11-digit or truncated number.
• The 7th digit combined with the 2-digit year encodes the birth century (per the official CPR table: 0-3 -> 1900s; 4/9 -> 2000s if YY<=36 else 1900s; 5-8 -> 2000s if YY<=57 else 1800s). Encodable date range is 1858-2057.
• The last (check) digit also carries sex: even = female, odd = male. In modulus-11 mode a requested sex is honored by redrawing until the forced check digit has the matching parity.

Gotchas

• Since 2007 the CPR office stopped guaranteeing the mod-11 check because valid serials were running out for some dates; the generator's 'none' checksum mode models these post-2007 numbers by drawing the last digit freely (correct parity only), so a real modern CPR may legitimately FAIL this mod-11 test.
• Leading zeros are significant — CPR numbers are handled as strings throughout (toDigits enforces a digit string) and must never be parsed through Number, or dates like 01xxxx would lose their leading zero.
• The check digit has weight 1, not a positional weight from the head; the [4,3,2,7,6,5,4,3,2] weights cover only the first nine digits.