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If the private key is lost, the bitcoin network will not recognize any other evidence of ownership;[9] the coins are then unusable, and effectively lost. For example, in 2013 one user claimed to have lost 7,500 bitcoins, worth $7.5 million at the time, when he accidentally discarded a hard drive containing his private key.[51] A backup of his key(s) would have prevented this.[52]
Miners are getting paid for their work as auditors. They are doing the work of verifying previous Bitcoin transactions. This convention is meant to keep Bitcoin users honest, and was conceived by Bitcoin’s founder, Satoshi Nakamoto. By verifying transactions, miners are helping to prevent the “double-spending problem.” 
To be accepted by the rest of the network, a new block must contain a so-called proof-of-work.[46] The system used is based on Adam Back’s 1997 anti-spam scheme, Hashcash.[5][54] The PoW requires miners to find a number called a nonce, such that when the block content is hashed along with the nonce, the result is numerically smaller than the network’s difficulty target.[4]:ch. 8 This proof is easy for any node in the network to verify, but extremely time-consuming to generate, as for a secure cryptographic hash, miners must try many different nonce values (usually the sequence of tested values is the ascending natural numbers: 0, 1, 2, 3, …[4]:ch. 8) before meeting the difficulty target.
To heighten financial privacy, a new bitcoin address can be generated for each transaction.[89] For example, hierarchical deterministic wallets generate pseudorandom “rolling addresses” for every transaction from a single seed, while only requiring a single passphrase to be remembered to recover all corresponding private keys.[90] Researchers at Stanford University and Concordia University have also shown that bitcoin exchanges and other entities can prove assets, liabilities, and solvency without revealing their addresses using zero-knowledge proofs.[91] “Bulletproofs,” a version of Confidential Transactions proposed by Greg Maxwell, have been tested by Professor Dan Boneh of Stanford.[92] Other solutions such Merkelized Abstract Syntax Trees (MAST), pay-to-script-hash (P2SH) with MERKLE-BRANCH-VERIFY, and “Tail Call Execution Semantics, have also been proposed to support private smart contracts.[93]
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