https://www.reddit.com/r/AskHistorians/comments/3ata56/why_666_for_the_beast_without_a_base10_positional/ Here's a prior thread featuring /u/talondearg and /u/Astrogator.

The short and sweet of it is that the number comes from the book of Revelations, where the reader is instructed to "calculate the number of the beast, for it is a human number, and its number is 666 [or 616 in some manuscripts]". This refers to the practice of Gematria, calculating numbers from the letters used to spell words. The most common explanation relies on transliterating the greek Neron Kaisar into Hebrew (NRWN QSR) - thus, the number refers to Emperor Nero. This works particularly well because N, "nun", is worth 50, so if you translate "Nero Caesar" from Latin, you get instead "NRW QSR", which adds up to 616, the other number present in some manuscripts. But as /u/talondearg goes into in the link, there are some problems with it.