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My understanding is that bitcoins were created to reward miners for keeping the network up and running. The blockchain is the main idea, bitcoins are simply a tool to incentivize people to run mining nodes and keep the network intact. I could be wrong though.

Only the bitcoin block-chain. That's for bitcoin and Counterparty assets

It's the oposite, Satoshi Nakamoto wanted to create digital P2P money. And then, as a solution to solve the double spending problem he came up with the idea of the blockchain as suplement of bitcoin, as the force behind it. But again we would not have a blockchain without bitcoin