21 days is possible, but you would need to have read the theory before you go out. Last year I completed my PPL in 21 days, including taking the exams. I had completed all the study prior though.
Most of the people I was flying with also completed on time however approx 30% failed to finish in 21 days.
It depends on your preperation and how you pick up the skills you are taught, along with some luck with the weather.