how many different types of aircraft ..?

I've always wondered how many different types of aircraft there have been since the Wright brothers first flew. By aircraft I mean heavier-than-air 'vehicles' such as helicopters, gliders etc. As for types of aircraft, exclude all variants unless of course they were 'different'  ie Spitfire and Seafire (two types) but include 'one-offs' like the Rutan Boomerang. I wonder if anyone has ever bothered to compile a list? I have a "Complete Encyclopedia of World Aircraft" (2002 editon). It includes helicopters but not balloons or gliders and runs to 925 pages and has about 2 or 3 models per page. (variants are listed for each model, for example there are 18 variants listed for the Fairchild C-82 Packet/C-119 flying boxcar). So  if the question is limited to commercial (no homebuilts) airplanes (and not dirigables, etc), and count the variants as one model, I'm guessing the number may be less than 5,000.