TinyURL
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In my introduction, I wrote, "it's even more than that, should they choose to have URLs with unique identifiers of between 1 and 6 characters". Reading this made me wonder: does TinyURL do this? And if so, what's the first TinyURL? http://tinyurl.com/0 doesn't exist (so subtract 1 from my answer ;-) but http://tinyurl.com/1 does. It is kind of fun to check out all these other people's URLs. http://tinyurl.com/z is pretty amusing.
I also realized that TinyURL's identifier is basically just counting in base 36. Ah, the ease of constructing unique IDs if they don't have to be hard to guess. 1...2...3...4...5...6...