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I am creating an Ether paper wallet using https://www.myetherwallet.com. I downloaded the source and I am running it offline. When I create a wallet I get an address such as 6d0715273557f1989F874623bdD1C7b174ad6F99. I can verify there is 0 ether in there using https://etherchain.org/. I want to ask, how is this wallet actually created? I created it offline so wondering how I now have this address that I can send and withdraw either from. How does it know which key to expect when withdrawing funds if I never sent the information before?

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What essentially happens is a a random private key is generated, from which the public key can be derived through cryptographic functions. As they key is randomly generated, it is statistically very unlikely to already be in use. All possible key pairs can theoretically exist on the blockchain. When you are using etherchain to find the balance of the address you are searching for, etherchain does not find any transactions in or out of the address, which is why it shows a zero balance.

When you send Ether to the new account, a transaction with a reference to your account address will be created, which a blockchain explorer such as etherchain will pick up on. This link may help you to understand the theory a little better, it refers to bitcoin but the principles are mostly the same.

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