Originally, I was going to call this article The mark of the beast, but such a title gives the wrong emphasis to John's vision. The mark and number of the beast may end Revelation 13, but this section flows into the next five verses, actually ending in 14:5.
And I saw a beast... (13:1)
Then I saw another beast... (13:11)
Then I looked, and there was the Lamb... (14:1)
Christians have given far too much time to deciphering 666, "the number of the beast" (13:18), and debating who it refers to (usually popes, presidents, or dictators, and always someone in the "opposition party" at the time). But, by focussing on this, we miss the larger picture where John asks in 13:4, "Who is like the beast, and who can fight against it?" and then answers in 14:1-5 by describing the lamb and an army like no other.
The identity of the beast as this or that world leader is really a non-event. It doesn't matter in the scheme of the letter. And if it did, I think John would point the finger at one of the Roman Caesars known by the original audience of the first century. How could John expect them to "calculate" (13:18 NRSV) it otherwise?
I'm with Ted Grimsrud when he talks about how triple sixes emphasise how human empires will always fall short of God's peace and wholeness.
The number 666 symbolises something more general—human culture organised to resist God. The six is just short of the number of wholeness (that is, the number seven); three sixes emphasise the failure.
— Ted Grimsrud
To Follow the Lamb, p.152
Following Daniel's example (see Dan. 7), John imagines human empires taking the shape of hideously twisted monsters that represent, like the number of the beast, how far short they are from God's purpose for humankind. Where the empire (or kingdom or basileia) of Jesus is one of self-giving love and nonviolent resistance, the empires of this world are self-serving and violent oppressors of land and people.
The more important number
The more important theological number is the 144,000 that John talks about at the beginning of Revelation 14.
Then I looked, and there was the Lamb, standing on Mount Zion! And with him were one hundred forty-four thousand who had his name and his Father's name written on their foreheads.
— Revelation 14:1 NRSV