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The words "Vacarius Filii Dei" contain letters which were also used as Roman numerals; these include V, C, I, L and D
There is 1 x V in the words. V has a value of 5.
There is 1 x C in the words. C has a value of 100.
There is 1 x D in the words. D has a value of 500.
There is 1 x L in the words. L has a value of 50.
There are 5 x I in the words. I has a value of 1, so 5 x I = 5.
In Roman Latin the Letter V was used for U, so it too would have represented 5.
If you add these values together you get; 500 + 100 + 50 + 5 + 5 + 5 = 665 (not 666). I also doubt that Filii ended in double I, if it were spelled Fili or Filis the total value would drop to 664.

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