Question

Is it common or worth anything to find 2 bills that were printed one after another?

For example... one is serial # 11111111 the other is 11111112

 

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Yes, it is not uncommon to obtain two or more notes in sequence. I typically get consecutive $1 banknotes in change, and some banks even distribute consecutive $20 notes.
Depends what year the note was printed also- I have 3 consecutive 1976 $2s, which you most likely won't find today.
$2 notes from 2013, however, are incredibly easy to find (it's almost impossible to find $2 notes that are not consecutive).

 

Ok great,thanks for the info @Legomaster1

 

Exactly what @Legomaster1 said.

 

If you do find those, however, you have hit the jackpot.

 

That was my thought - wouldn't they be consecutive Binaries?

 

other than binaries ans such,
one can obtain strapped money from their bank/cu, which would be one hundred consecutive serial numbers. I've never bought a "block" which could technically be a whole bunch of consecutives.