You say you only had it 4 days.Do you know the previous owner well??
Has been done before ,as the person you bought it off knows where you live due to log book having to be posted by him and he,s probably got a spare set of keys.

Was it on the drive/garaged,stolen night /day.?
Also were you insured so you can at least get some money back?
Hope you find it ,but as you've said the thieving scum will prabaly get away with it.