The end of TinyURL?

Lately –especially since I use Twitter– I receive a lot of URLs in TinyURL format. That made me think: if TinyURL gives out a unique URL each time it is used, when will they run out of URLs?
On their site they state that they have more than 42 million of them, which doesn’t sound like an awful lot. All TinyURLs I receive have a six character identifier, such as **3bso2z**. A little calculation (six positions with 36 options per position) gives me 2.238.976.116 unique identifiers. More than two billion, that sounds already better. And if they run out of Ids, they can simply use seven or eight characters, which I still consider tiny. Eight positions give 2.984.555.162.628 (2 trillion!) unique identifiers!
It is clear: TinyURL is here to stay.