Six is the number of man. It is noticeably one short of the number of God (7).
Man was created on the sixth day (Genesis 1:24).
Also, the Babylonians (often the model of human centered society) were facinated with 6, and 60's, and 600's. Our system for time is influenced by them (60 second minutes, minutes in hours, 360 (6 x 60) + some days per year, 360 degrees, etc.)
As, I mentioned earlier, the number of the ultimate (final) man is 666 (Revelation 13:18).