Q. What is the significance of the individual numbers of the satellite code number: 4, 8, 15, 16, 23, 42?
A. There is no intrinsic significance of the numbers beyond the show. They are not an obscure occult reference or have any scientific/mathematical relevance whatsoever. They are the passcode that stops the satellite from zapping the hatch - the security system to protect the island and its secrets. Within the realms of me making things up about Lost: the fact that the numbers get larger suggests arithmetic progression; the numbers are minutes adding up to 108 minutes (the time it takes the satellite to orbit the earth); the satellite is asked to perform a task at 4 minutes, then 8 minutes later, then 15 minutes later and so on, but what that is probably doesn't matter.
This is pretty deep. So a satellite in orbit passes directly over the island every 108 minutes. It is instructed to perform 'tasks' at time intervals of 4, 8, 15, 16, 23, and 42 minutes during it's orbit. Wonder what geographic points of the globe the satellite might pass over at these intervals? Specific global regions of power, to support information gathering or electromagnetic disruption tasks for the world peace initiative.
So say they are on an island in the pacific, which seem a reasonable guess, then the 4 and 12 minute marks of orbit could be west/east coast north america.
4 = West coast N.A.(L.A./Seattle/Silicon Valley)
12(4+8) = East coast N.A.(Washington D.C./NYC)
27(4+8+15) = Western Europe(London/Paris, perhaps Berlin)
43(4+8+15+16) = Moscow/Middle East
66(4+8+15+16+23) = Bejing/Tokyo
108(4+8+15+16+23+42) = LOST Island.