Why is 666 the number of the beast? Is it symbolic? Is the mark simply the fact that these people worship Satan and, therefore, not an actual visible body marking, such as a tattoo or colored skin?
I have suggested elsewhere the significance of the number 6 in scriptures. Especially in the book of Revelation, where you find symbolic representation in stones, earthly objects, heavenly actors, and acts of nature, it comes as no surprise that numbers take on special meaning.
The number 6 as a symbol suggests an imperfect creation, a fallen man. The number 666, then, triply emphasizes such a carnal, natural man. Indeed, the beast mentioned in Revelation turns men away from God, controls the economy, and wields the power of capital punishment (Rev 13). But despite the imagery of a beast that John uses, the Revelator wants us to know that he is writing about a specific man. “[T]he number of the beast,” he clarifies, “is the number of a man,” playing on the number as a symbol of man at enmity with God, as well as pointing us towards gematria.
Most uses of gematria that you will find are absolute rubbish. In Hebrew, the letters also doubled as numbers so you can literally sum words or the letters of a word together. You can take that a step further and break those numbers down to create a sort of horoscope for a word, sentence, or name. I would caution against taking this too far (just as some would take other symbols too far, and see in them signs that aren’t there). That being said, it appears that John is pointing us down this path as a confirmation (not necessarily as the positive id) of the second beast. Modern scholars suppose it to have been the Emperor Nero (who was notoriously anti-Christian), whose throne name “Neron Caesar” when transliterated to Hebrew had the gematria of 666.
Undoubtedly, this symbol has significance in the latter days, but as with all other symbols in this book we await the day when the meaning will be made clear through revelation. Joseph Smith taught, “whenever God gives a vision of an image, or beast, or figure of any kind, He always holds Himself responsible to give a revelation or interpretation of the meaning thereof, otherwise we are not responsible or accountable for our belief in it” (Teachings of the Prophet Joseph Smith 291).
As to whether it is a visible mark, apparently it is. Elder Bruce R. McConkie asks the same question, and answers it in this way-
“And the first went, and poured out his vial upon the earth; and there fell a noisome and grievous sore upon the men which had the mark of the beast, and upon them which worshipped his image.” Could this be the same plague of which Zechariah speaks when he says that men’s “flesh shall consume away while they stand upon their feet, and their eyes shall consume away in their holes, and their tongue shall consume away in their mouth”? (Zech. 14:12).
Does it have reference to these words of latter-day revelation:
“And their flesh shall fall from off their bones, and their eyes from their sockets”? (D&C 29:19).
Is this a plague that will result from atomic fallout? Or from some worldwide pollution of the air we breathe, the food we eat, and the water we drink? It is to come upon those who worship at the altars of evil, leaving the inference that those only will escape who have faith in the Lord and who exercise the power of the priesthood to rebuke the evils that otherwise would afflict them (The Millennial Messiah, p.394).