It is 24 working days and since Saturdays count as working days: 24 / 6 = 4
It is called "Bundesurlaubsgesetz" -- my translation: Federal Vacation Law.
Does anything like that exist somewhere else?
Generally, if you live in the southern part of Germany, you also get several catholic hol(i|y)days, no matter if you are catholic or not.
Depending on the state you are living in you also get between 9 and 13 holidays. Some of those will fall on weekends from time to time but six weeks (30 days) of paid vacation seem not all that unrealistic in a good year (i.e. many holidays not on weekends) if you live in Bavaria (that’s the state with the 13 holidays, eight of them not on weekends in 2010, ten in 2011, twelve in 2012 – some great years coming up ;-).