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Can you tell me why the numbers 666 was used to describe the beast and not the numbers 777?
Any reason I can give for the number 666 specifically being used as the number of the beast would be a guess. The closest I can come to an answer from the Bible is that it says this is the number of a man. This would probably be a man who was then ruling (or recently ruled), and based on the Hebrew letters in that name. The name of Nero Caesar fits this requirement. Had Nero’s name totalled any other number then that might have been the number of the beast instead of 666.
Others have suggested that 777 would indicate perfection so 666 was used to indicate less than perfection. This may be true, but that is pure speculation. The first theory fits the facts better.
In addition to the response above, I should point out that the number in Revelation 13:18 is not six-six-six but 600+60+6. It's connection to the number six is in multiples, not in repetition. Thus, some people's fear of any number containing three consecutive sixes is groundless. That is, the number 6,660 has no relationship to the number of the beast. In fact, if you were to convert the number of the beast to a binary system, such as is used in computers, it would not be written 666 but 1010011010. I wonder if those who worry about the number 666 react in the same way to all the variations of the number in different bases. I doubt it. For instance, would anybody who used a 30/30 rifle or pistol be considered the beast, since 3030 is the number in base 6? Here we begin to get a little ridiculous.