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Yup, they do! Twitter has hard-coded all banned passwords on the sign-up page. All you need to do to retrieve the full list of ‘too obvious‘ passwords is take a look at the source code of that page.
In reality, the control is placed directly into the source of the registration page, to find just look inside the string twttr.BANNED_PASSWORDS.
A total of 370 passwords are prohibited while signing up to Twitter; Among them the trivial password, 123456, and other combination of simple numbers, plus many more that TechCrunch has stored the collected password into a text file.