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Given a particular ethereum account address, can we find out if it is from the main-net or the test-net?

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An Ethereum address is a 40 character hex encoded string.

It can be easily converted to a public key. Each public key has a corresponding private key (which should be kept private).

Given that the testnet and mainnet run using the same codebase, the cryptographic functions which work with and manipulate these addresses are the same.

A blockchain is a ledger of transactions. Whilst a mist keyfile (for example) works on either network, each network has a different ledger of transactions. If you have 100 Ether in account 0xdead on Ropsten, you will not have the same amount on the Mainnet.

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You account is generic and valid for every network, so there's not any difference.

What's the difference between the `testnet` and the production network technically?

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