Q: How many unique Tweets can ever be posted?

At least  (a number with 1,264 decimal digits), using the contents of the tweet alone. Plus there is all the metadata, which probably adds at least a thousand bits.

See https://blogs.oracle.com/ksplice... . It turns out that Twitter allows almost 2^31 choices per "character," at least when a tweet is first posted. (They decay over time...)

Unicode itself is a 20.1-bit system, but Twitter doesn't allow literally all Unicode scalar values. (E.g. it messes with < and >.) On the other hand, Twitter does allow the huge characters above the first 2^20, that is to say not Unicode, but below 2^31. (This is almost 31 bits anyway.)

Disclaimer: I have not checked this myself since writing that blog post in March 2010.