Assuming that (1) you were born between 1950 and 1985 and (2) the danish date format is (dd-mm-yy), here are the possible DOBs:
10-01-51 30-01-51 17-03-51 14-05-51 26-05-51 27-05-51
13-06-51 16-06-51 16-07-51 18-07-51 25-07-51 25-09-51
15-10-51 21-10-51 24-10-51 21-11-51 13-12-51 17-12-51
19-12-51 28-12-51 10-01-53 17-03-53 27-05-53 16-07-53
25-07-53 21-11-53 17-12-53 24-02-57 29-06-57 25-10-57
13-02-59 24-02-59 21-03-59 29-06-59 14-07-59 17-07-59
22-08-59 15-09-59 25-10-59 26-10-59 10-11-59 24-12-59
13-02-61 10-03-61 21-03-61 31-03-61 27-04-61 23-05-61
14-07-61 17-07-61 27-07-61 22-08-61 23-08-61 26-08-61
15-09-61 12-10-61 18-10-61 21-10-61 26-10-61 10-11-61
17-11-61 24-12-61 25-12-61 10-03-63 31-03-63 27-04-63
23-05-63 27-07-63 23-08-63 26-08-63 12-10-63 18-10-63
21-10-63 17-11-63 25-12-63 13-03-67 19-03-67 11-05-67
19-06-67 15-07-67 14-08-67 20-08-67 16-09-67 25-09-67
24-10-67 17-11-67 26-11-67 29-11-67 27-02-69 13-03-69
17-03-69 19-03-69 22-04-69 11-05-69 19-06-69 29-06-69
15-07-69 28-07-69 14-08-69 20-08-69 16-09-69 25-09-69
22-10-69 24-10-69 12-11-69 15-11-69 17-11-69 26-11-69
29-11-69 11-12-69 23-12-69 27-02-71 17-03-71 22-04-71
29-04-71 29-06-71 23-07-71 28-07-71 22-10-71 12-11-71
15-11-71 22-11-71 11-12-71 23-12-71 29-04-73 23-07-73
22-11-73 15-03-77 11-04-77 19-05-77 16-08-77 22-08-77
17-10-77 25-11-77 27-12-77 18-01-79 15-03-79 11-04-79
19-05-79 11-08-79 16-08-79 22-08-79 17-10-79 14-11-79
25-11-79 10-12-79 27-12-79 18-01-81 20-03-81 16-04-81
30-05-81 14-06-81 11-08-81 15-08-81 24-08-81 14-11-81
30-11-81 10-12-81 20-03-83 16-04-83 30-05-83 14-06-83
15-08-83 24-08-83 30-11-83Thanks for the list but he said 6 digits... So the format is probably dd-mm-yy.
Oops! Corrected.
Impossible? Danes write dates as dd-mm-yy according to http://en.wikipedia.org/wiki/Calendar_date, so your birthday can have at most one leading zero and thus is >= 10100. 9973 is the largest 4-digit prime number, and 9973 + 2 is 1) not prime and 2) not a 5-digit number.
We're talking about two sets of twin primes, each part of the social security number being in each set. I'm sorry I didn't make it clear in the OP.
Now someone can guess your entire social security number :P
Calculated risk
Assuming you're talking about splitting your SSN down the middle (two 5 digit numbers) and it looks something like this
http://en.wikipedia.org/wiki/Personal_identification_number_...
The candidates are (unless I horked something up, these are pairs of 5 digit twin primes that start with a sensible 6 digit date and checksum as Danish SSNs)
0212702129 0608706089 2105721059 2210722109
That's assuming you were not born in '90 or '91.
My two numbers aren't only prime, which in and of itself would be pretty unlikely. No they're Twin primes. (http://en.wikipedia.org/wiki/Twin_prime)
This is the only place I know where information like that would be considered pretty cool :-)
Now somebody guess my birthday.