So, this thread made me think of the interesting problem of exactly how many possible usernames there are!

I've come up with 342,708,664,283,810,176,729,802 - that's 342 [b]sextillion[/b], 3.42*10^23 possible names.

I don't think we have to worry about running out of names any time soon - there are enough for each person alive to have [b]billions[/b] of usernames.

Also, I bet you just glossed over that huge number when you read it.

[hider=Maths]
How did I come up with that number?

Well, first, your username on the guild has to be from two to fifteen characters long.
Second, possible characters include a space, A-Z, and 0-9. It seems that capitalization does not matter, so Alex ALex alEX are all the same username (try logging in with strange capitalization). So 26 letters, ten numbers, and a space gives us 37 possible characters to work with.

The number of different usernames that can exist with two characters can be represented by
37*37
So, you can put any of our 37 characters in the first spot and any of the 37 characters in the second spot. (This isn't technically true - you can't have a name that has only spaces [i tried), and I bet you can't have a space preceding or following your username, usernames that are offensive and would be banned, and so on - but I think that these special cases aren't significant enough to really change that big number up at the top by a large amount.)

So then, we can see that the number of usernames that can exist for any length [i]k[/i] is 37^k.
So if we added up all the answers for k=2 and k=15...

Wait, this sounds like a [url=https://en.wikipedia.org/wiki/Geometric_series]geometric series[/url]!
In particular, this helps greatly:
[url]https://upload.wikimedia.org/math/0/2/9/029e68ec4c3a9c97b61c6d5b011efcfd.png[/url]
Replacing the pertinent numbers into the equation gives us:

(37^2-37^(15+1))/(1-37)
If you drop that into google, you'll get a number similar to what I have up top. I just calculated it out all the way.
[/hider]

Doing all that math reminded me of something I was working on a few weeks ago - someone on the IRC told me about [url=https://libraryofbabel.info/]The Library of Babel[/url] project, which apparently contains everything ever written (within the parameters they have currently). I was trying to figure out how large the library would have to be in meatspace (And now I realize I was going at it the wrong way!)

(p.s. if i'm wrong feel free to correct me i'd love to know what I messed up)