To be accepted by the rest of the network, a new block must contain a proof-of-work (PoW).[75] The system used is based on Adam Back's 1997 anti-spam scheme, Hashcash.[85][4] 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.[7]: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, ...[7]:ch. 8) before meeting the difficulty target.
According to the European Central Bank, the decentralization of money offered by bitcoin has its theoretical roots in the Austrian school of economics, especially with Friedrich von Hayek in his book Denationalisation of Money: The Argument Refined,[127] in which Hayek advocates a complete free market in the production, distribution and management of money to end the monopoly of central banks.[128]:22

Ethereum’s core innovation, the Ethereum Virtual Machine (EVM) is a Turing complete software that runs on the Ethereum network. It enables anyone to run any program, regardless of the programming language given enough time and memory. The Ethereum Virtual Machine makes the process of creating blockchain applications much easier and efficient than ever before. Instead of having to build an entirely original blockchain for each new application, Ethereum enables the development of potentially thousands of different applications all on one platform.
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There is ongoing research on how to use formal verification to express and prove non-trivial properties. A Microsoft Research report noted that writing solid smart contracts can be extremely difficult in practice, using The DAO hack to illustrate this problem. The report discussed tools that Microsoft had developed for verifying contracts, and noted that a large-scale analysis of published contracts is likely to uncover widespread vulnerabilities. The report also stated that it is possible to verify the equivalence of a Solidity program and the EVM code.[41]
Like Bitcoin, Ethereum is a distributed public blockchain network. Although there are some significant technical differences between the two, the most important distinction to note is that Bitcoin and Ethereum differ substantially in purpose and capability. Bitcoin offers one particular application of blockchain technology, a peer to peer electronic cash system that enables online Bitcoin payments. While the Bitcoin blockchain is used to track ownership of digital currency (bitcoins), the Ethereum blockchain focuses on running the programming code of any decentralized application.
The rapid price increase of Ethereum has not only attracted investors but developers too. Ethereum has tens of thousands of developers in its open source community, each contributing to the many layers of the “Ethereum stack”. This includes code contributions to the core Ethereum clients, second layer scaling tech and the “decentralized applications” (dApps) that are built on top of the platform. The appeal of Ethereum to developers is unique in that it was the first platform to allow anyone in the world to write and deploy code that would run without the risk of censorship. The community of developers which have formed around these core principles have led to the creation of technologies that could not have existed without the inception of Ethereum, many of which were never predicted. Some of the major use-cases of Ethereum so far have been:

Bloomberg reported that the largest 17 crypto merchant-processing services handled $69 million in June 2018, down from $411 million in September 2017. Bitcoin is "not actually usable" for retail transactions because of high costs and the inability to process chargebacks, according to Nicholas Weaver, a researcher quoted by Bloomberg. High price volatility and transaction fees make paying for small retail purchases with bitcoin impractical, according to economist Kim Grauer. However, bitcoin continues to be used for large-item purchases on sites such as Overstock.com, and for cross-border payments to freelancers and other vendors.[141]
Blockchain analysts estimate that Nakamoto had mined about one million bitcoins[28] before disappearing in 2010, when he handed the network alert key and control of the code repository over to Gavin Andresen. Andresen later became lead developer at the Bitcoin Foundation.[29][30] Andresen then sought to decentralize control. This left opportunity for controversy to develop over the future development path of bitcoin, in contrast to the perceived authority of Nakamoto's contributions.[31][30] 
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