Citizen Paul,
There are some quite old threads on details of Culture, that you might be able to find. For 100 Culture, you need perfect ratings for theaters and education buildings plus enough religious buildings to the keep the gods happy without festivals: any combination of 1 oracle for 500 people, 5 small temples to each god for 750 people, and 5 large temples to each god for 1500 people. Lesser numbers of any of these buildings give some contribution to Culture, but I'm not sure of the details. I think religion counts a lot (maybe 30%) and academies a little (maybe 10%).
paultheo,
Even using a simple average, 100 Prosperity is possible in a city with just large tents and luxury palaces in an 18:1 ratio. If the prosperity cap was a population-weighted average, it would be ridiculous: 100 Prosperity with 1 luxury palace and 3666 people living in large tents.
Jayhawk,
That's not a well-defined problem. Using the kind of micromanagement techniques Nerdicus has been discussing at Pharaoh Heaven, the number could be quite small. Assuming that you want a stable village, the fewest people would be needed with all foods and goods imported, and 1 building for most of the services (except hippodrome, academy, hospital, and maybe amphitheater or theater). I'd guess that paultheo is close, although no palaces are needed, since 1 (or maybe 2) small villas would be enough patricians with plebians in grand insulaes.