(Re 13:18) Here is where wisdom comes in: Let the one that has intelligence calculate the number of the wild beast, for it is a man's number; and its number is six hundred and sixty-six.
A number to be calculated
TThere's nothing evil about the digits 6, 6 and 6. A house at 666 Main Street isn't cursed. Revelation was written in signs, so the number stands for something that can actually be calculated out to six hundred and sixty-six, and the verse tells us two things about it. It's a man's number, which puts it in the visible, measurable world. And it can be calculated, which means God expects us to work it out from the clues he gave.
When the verse says "Let the one that has intelligence calculate," it's an invitation, not a riddle set to frustrate anyone, and Jehovah doesn't invite people to do something he's given them no means to do. So the clues have to be there, in the scriptures and in the history the scriptures record.
Where the number first shows up
Revelation isn't where the number first appears. Nebuchadnezzar's image of gold on the plain of Dura stood sixty cubits high on a base six cubits wide (Daniel 3:1), and all peoples were commanded to worship it or die (Daniel 3:4-6). Read Revelation 13 beside that scene and every piece is back: an image, forced worship, death for refusing, and the number 666. The image in Daniel foreshadows the image of the beast.
How this site counts it
The study series on the mark of the beast follows the false god Saturn through all seven heads of the beast. It starts at the golden calf Apis and ends at the star of Rephan named at Amos 5:26 and Acts 7:43, and it identifies that star as the six-pointed star inside the ouroboros. The last part plots the digital roots of the mitosis sequence and mirrors them, and the star of Saturn appears. The sum of the numbers from 1 to 36 is 666. Counting sixes in a hexagram's points, sides and corners was always an arbitrary way to read it. This series reaches the same number by a different road, one that begins in Israel's own history of false worship.