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In the blockchain, bitcoins are registered to bitcoin addresses. Creating a bitcoin address requires nothing more than picking a random valid private key and computing the corresponding bitcoin address. This computation can be done in a split second. But the reverse, computing the private key of a given bitcoin address, is mathematically unfeasible. Users can tell others or make public a bitcoin address without compromising its corresponding private key. Moreover, the number of valid private keys is so vast that it is extremely unlikely someone will compute a key-pair that is already in use and has funds. The vast number of valid private keys makes it unfeasible that brute force could be used to compromise a private key. To be able to spend their bitcoins, the owner must know the corresponding private key and digitally sign the transaction. The network verifies the signature using the public key.[3]:ch. 5
To heighten financial privacy, a new bitcoin address can be generated for each transaction.[113] 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.[114] Researchers at Stanford and Concordia universities have also shown that bitcoin exchanges and other entities can prove assets, liabilities, and solvency without revealing their addresses using zero-knowledge proofs.[115] "Bulletproofs," a version of Confidential Transactions proposed by Greg Maxwell, have been tested by Professor Dan Boneh of Stanford.[116] 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.
On 1 August 2017, a hard fork of bitcoin was created, known as Bitcoin Cash.[103] Bitcoin Cash has a larger block size limit and had an identical blockchain at the time of fork. On 24 October 2017 another hard fork, Bitcoin Gold, was created. Bitcoin Gold changes the proof-of-work algorithm used in mining, as the developers felt that mining had become too specialized.[104]
Our first assumption is that bitcoin will derive its value both from its use as a medium of exchange and as a store of value.  As a footnote to this assumption, it should be stated that bitcoin's utility as a store of value is dependent on its utility as a medium of exchange.  We base this in turn on the assumption that for something to be used as a store of value it needs to have some intrinsic value, and if bitcoin does not achieve success as a medium of exchange, it will have no practical utility and thus no intrinsic value and won't be appealing as a store of value.    
The other reason is safety. Looking at 2009 alone, 32,489 blocks were mined; at the then-reward rate of 50 BTC per block, the total payout in 2009 was 1,624,500 BTC, which at today’s prices is over $900 million. One may conclude that only Satoshi and perhaps a few other people were mining through 2009, and that they possess a majority of that $900 million worth of BTC. Someone in possession of that much BTC could become a target of criminals, especially since bitcoins are less like stocks and more like cash, where the private keys needed to authorize spending could be printed out and literally kept under a mattress. While it's likely the inventor of Bitcoin would take precautions to make any extortion-induced transfers traceable, remaining anonymous is a good way for Satoshi to limit exposure.
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Another interesting way (literally) to earn bitcoins is by lending them out, and being repaid in the currency. Lending can take three forms – direct lending to someone you know; through a website which facilitates peer-to-peer transactions, pairing borrowers and lenders; or depositing bitcoins in a virtual bank that offers a certain interest rate for Bitcoin accounts. Some such sites are Bitbond, BitLendingClub and BTCjam. Obviously, you should do due diligence on any third-party site.
Satoshi Nakamoto is credited with designing Bitcoin. Nakamoto claims to be a man living in Japan born on April 5th, 1975 but there are speculations that he is actually either an individual programmer or group of programmers with a penchant for computer science and cryptography scattered around the United States or Europe. Nakamoto is believed to have created the first blockchain database and have been the first to solve the double spending problem other digital currency failed to. While Bitcoin’s creator is shrouded in mystery, his Wizard of Oz status hasn’t stopped the digital currency from becoming increasingly popular with individuals, businesses, and even governments.

A wallet stores the information necessary to transact bitcoins. While wallets are often described as a place to hold[87] or store bitcoins,[88] due to the nature of the system, bitcoins are inseparable from the blockchain transaction ledger. A better way to describe a wallet is something that "stores the digital credentials for your bitcoin holdings"[88] and allows one to access (and spend) them. Bitcoin uses public-key cryptography, in which two cryptographic keys, one public and one private, are generated.[89] At its most basic, a wallet is a collection of these keys.
One of the first supporters, adopters, contributor to bitcoin and receiver of the first bitcoin transaction was programmer Hal Finney. Finney downloaded the bitcoin software the day it was released, and received 10 bitcoins from Nakamoto in the world's first bitcoin transaction on 12 January 2009.[21][22] Other early supporters were Wei Dai, creator of bitcoin predecessor b-money, and Nick Szabo, creator of bitcoin predecessor bit gold.[12] 

Our second assumption is that the supply of bitcoin will approach 21 million as specified in the current protocol.  To give some context, the current supply of bitcoin is around 17 million, the rate at which bitcoin is released decreases by half roughly every four years, and the supply should get past 19 million in the year 2022.  The key part of this assumption is that the protocol will not be changed.  Note that changing the protocol would require the concurrence of a majority of the computing power engaged in bitcoin mining. (Related: How Does Bitcoin Mining Work?)
“It has long been thought that for something to be a useful currency, it needs to be a stable source of value, and bitcoin is anything but. It’s not used for a lot of transactions, it’s not a stable source of value, and it’s not an efficient means of processing payments. It’s very slow in handling payments. It has difficulty because of its very decentralized nature.”
Meanwhile, investors have been rattled this week by reports bank-owned currency trading utility CLS, along with enterprise software giant IBM, are teaming up to trial the blockchain-based Ledger Connect, an application that offers services from different vendors, with some nine financial institutions, including international heavyweights Barclays and Citigroup.
The simplest way to approach the model would be to look at the current worldwide value of all mediums of exchange and of all stores of value comparable to bitcoin, and calculate the value of bitcoin's projected percentage.  The predominant medium of exchange is government backed money, and for our model we will focus solely on them.  The money supply is often thought of as broken into different buckets, M0, M1, M2, and M3.  M0 refers to currency in circulation.  M1 is M0 plus demand deposits like checking accounts.  M2 is M1 plus savings accounts and small time deposits (known as certificates of deposit in the US).  M3 is M2 plus large time deposits and money market funds.  Since M0 and M1 are readily accessible for use in commerce, we will consider these two buckets as medium of exchange, whereas M2 and M3 will be considered as money being used as a store of value.
In its October 2012 study, Virtual currency schemes, the European Central Bank concluded that the growth of virtual currencies will continue, and, given the currencies' inherent price instability, lack of close regulation, and risk of illegal uses by anonymous users, the Bank warned that periodic examination of developments would be necessary to reassess risks.[179]

17-20 November 2017 $7,600-8,100 Briefly topped at USD $8004.59/BTC at 01:14:11 UTC before retreating from highs. At 05:35 UTC on 20 November 2017 it stood at USD$7,988.23/BTC according to CoinDesk.[165] This surge in bitcoin may be related to developments in the 2017 Zimbabwean coup d'état. The market reaction in one bitcoin exchange is alarming as 1 BTC topped nearly US$13,500, just shy of 2 times the value of the International market.[166][167]
Computing power is often bundled together or "pooled" to reduce variance in miner income. Individual mining rigs often have to wait for long periods to confirm a block of transactions and receive payment. In a pool, all participating miners get paid every time a participating server solves a block. This payment depends on the amount of work an individual miner contributed to help find that block.[82]
Bitcoin's journey continued slowly at first, but it hit the mainstream in 2013 after the first of several hyperinflation incidents occurred in the currency. In late 2013, the cryptocurrency spike in value from around $100 per coin to $1,000 in just over a month, before halving in value over the next three or four months. Bitcoin would not hit $1,000 again until 2017.

On 3 March 2014, Flexcoin announced it was closing its doors because of a hack attack that took place the day before.[211][212][213] In a statement that once occupied their homepage, they announced on 3 March 2014 that "As Flexcoin does not have the resources, assets, or otherwise to come back from this loss [the hack], we are closing our doors immediately."[214] Users can no longer log into the site.
Every 2,016 blocks (approximately 14 days at roughly 10 min per block), the difficulty target is adjusted based on the network's recent performance, with the aim of keeping the average time between new blocks at ten minutes. In this way the system automatically adapts to the total amount of mining power on the network.[3]:ch. 8 Between 1 March 2014 and 1 March 2015, the average number of nonces miners had to try before creating a new block increased from 16.4 quintillion to 200.5 quintillion.[80]