The question of what the "Number of the Beast" refers to in the Book of Revelation has been a disputed point for a very long time. While I have my suspicions, what actually is the Number of the Beast is not the point of this post. Instead, it's about what it is not.
The unfortunate thing is, a large percentage of what you see people suggest the Number of the Beast referring to are things that ignore the actual text of Revelation. One would think that what it actually says about the Number of the Beast would be paramount, but people so often ignore that.
Since the text is so important, let's look at it. The Number of the Beast is described in Revelation 13:17-18. Here is the text of those verses in several translations.
"...so that they could not buy or sell unless they had the mark, which is the name of the beast or the number of its name. This calls for wisdom. Let the person who has insight calculate the number of the beast, for it is the number of a man. That number is 666." (NIV)
"... and he decrees that no one will be able to buy or to sell, except the one who has the mark, either the name of the beast or the number of his name. Here is wisdom. Let him who has understanding calculate the number of the beast, for the number is that of a man; and his number is six hundred and sixty-six." (NASB)
"...and that no man might buy or sell, save he that had the mark, or the name of the beast, or the number of his name. Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six." (KJV)
"...so that no one can buy or sell who does not have the brand, that is, the name of the beast or the number for its name. This calls for wisdom: let anyone with understanding calculate the number of the beast, for it is the number for a person. Its number is six hundred sixty-six" (NRSV)
In footnotes, the NIV does note that "number of a man" could be rendered as "humanity's number", the NRSV notes that some manuscripts say "six hundred sixteen", and the NASB mentions both, but these are not particularly important for the point I am going to make (if you hold to the six hundred and sixteen, simply assume the rest of this post refers to that number). But we can see these agree on the critical points of translation. The Number of the Beast is six hundred and sixty six, it can be calculated, and it is from the Beast's name.
From this statement, we can draw two very clear points.
First, that the Number of the Beast is the numerical value of six hundred and sixty six.
Second, the Number of the Beast is the number of the name of the Beast.
With these two, we can instantly dismiss so many speculations on what it means. I'll explain.
I have seen so many people find three 6's (or sometimes two or four) together and try to find a connection to the Number of the Beast. 66, 66.6, 1666, 6666, 60606, and anything like that. One person I even saw appeal to an instance of 999, reasoning that upside down it's 666. Others try to focus on the way it is written in Arabic numerals (what we use in English), like one person who tried to offer an argument based on the fact it used the same numeral three times--ignoring the fact that in Greek, it was written ΧΞΣ. And speaking of the Greek, still others look at the Greek numerals and try to find some kind of a connection to things that look like those numerals or try to find a connection to the alphabetical letters, in both cases not focusing on the actual number (some manuscripts did actually write it out in word form, namely ΕΞΑΚΟΣΙΟΙ ΕΞΗΚΟΝΤΑ ΕΞ, but most do it in numerals).
These, however, do not fit with what is actually written. First, it is the numerical value of six hundred and sixty six. Any other number--whether it be sixty-six, sixty-six and six-tenths, one thousand six hundred and sixty six, six thousand six hundred sixty-six, or sixty thousand six hundred and six, or anything else, does not qualify.
The author of Revelation in fact emphasizes it is the number, for he says to calculate or count the Number of the Beast. This is done as if the author wanted to emphasize the point we are talking about the number and to make sure people did not come up with all of the interpretations that, unfortunately, they did so anyway. So anything that is not the number six hundred and sixty six and is not that exact number is disqualified. Stop obsessing over numbers that in Arabic numerals happen to look similar to 666 and focus only on the number. What matters is that the number is the integer that comes between 665 and 667 that is written as ΧΞΣ in Greek numerals, 666 in Arabic numerals, DCLXVI in Roman numerals, and 六百六十六 in Chinese/Japanese numerals. It's the number six hundred and sixty six.
Thus, if the interpretation doesn't involve an actual numerical value, and that numerical value isn't the number six hundred and sixty six, the interpretation should be discarded.
We next move onto the other important thing: The Number of the Beast is not something that is simply affiliated with the Beast, but is the number of the Beast's name. It explicitly says this in Revelation. This rules out a lot of other proposed interpretations. I have seen, for example, a number of people note that the amount of gold Solomon received in 1 Kings 10:14 and 2 Chronicles 9:13 was described as six hundred and sixty six, and there is also the fact that the sons of Adonikam in Ezra 2:13 were numbered as six hundred and sixty six. Through these--especially the Solomon one--speculations emerge, like saying it has something to do with money.
But this again runs against what Revelation actually says, which is that it's the number of the Beast's name. So we can see the Solomon instance can mean nothing; Solomon's name does not add up to that, and even if someone were to try to claim it somehow relates to the name of the currency, I am not aware of any currency whose name adds up to six hundred and sixty six (certainly not the currency mentioned there, which was gold talents). Simply seeing the number six hundred and sixty six somewhere means nothing in regards to Revelation unless it somehow comes from a name.
And that brings us to the end of this relatively short post. While I will not venture forward to proclaim what the Number of the Beast refers to, we can certainly see many of the things it is not. If someone offers an interpretation of it, and the number does not come from a name, and it is not the actual number of six hundred and sixty six, then their idea should be disregarded.