I really don't need a number to have proof that she's the
antichrist...but maybe the shiny green "666" on the dark, dark fur
will warn our visitors in our new place...

(Oddly, she's not that bad at the vet's or in the car.  Thrashing is
undignified and yowling makes you look a fool.  Far better to bite
your slaves in their sleep, eat their kleenex, exhume their sock
drawers, and drop lamps on their heads.  She is...a subtle evil.)

--Fil

The likeliest explanation that I have heard for both versions of this
number is that it is a reference to the emperor Nero.  From what I
have read, if you take the Latin version of his name, Nero, write out
a phonetic representation in Hebrew letters, and use the standard
correlation of letters to numbers, you get the value 616.  If you use
the Greek version of Nero's name, Neron, and do this transformation,
you get 666.

Given that the government persecution of the Christians started under
Nero, and that the Book of Revelations is thought to have been written
during his reign, the above explanation is certainly possible.