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Primary states are those state societies that formed without any influence from existing state societies, i.e. those civilizations which build themselves up from the ground up. Generally there are considered to be six:
Mesopotamia
Egypt
North India
North China
Mesoamerica
The Andes
Some anthropologists would argue that Hawaii and Tonga were also primary states, but they're different from the above six primarily due to their lack of urbanization and their much more rudimentary bureaucracies.
All other state societies--or "civilizations"--can trace themselves, directly or indirectly, to one or more of these six.