From the Revelation, "This calls for wisdom. If anyone has insight, let him calculate the number of the beast [the devil, or Satan], for it is man’s number. His number is 666."
One of the older interpretations for this is that the number 7 is God's number. The devil and people are constantly attempting to get to the number of God. Yet, they can't make it. All the farther they get is 6, 6, 6, every time they try.