The very first major jump in Bitcoin price took place in July 2010. At this point, the value of Bitcoin went from about $0.0008 all the way up to $0.08, a truly dramatic increase in price. At this point and in the following year, very few exchanges supported trading of Bitcoin. There was also extremely limited liquidity at this time due to cryptocurrency still being relatively unknown. That meant that when the price started an increase in June 2011 from about $0.95, the approach was among the steepest recorded. Unfortunately, the drop also followed suit. By mid-June of that year, Bitcoin was up to $320, an all-time high. By November, it had declined 94 percent all the way to $20.

It's impossible to say how much bitcoin has increased in price single its earliest incarnation, because its value back then was in the fractions of cents. A conservative estimate, based on bitcoin's current price being around $6,300 per coin, and its early price being less than $0.01, would see bitcoin's value increasing more than 1 million fold in the last decade.

It’s decentralized and brings power back to the people. Launched just a year after the 2008 financial crises, Bitcoin has attracted many people who see the current financial system as unsustainable. This factor has won the hearts of those who view politicians and government with suspicion. It’s no surprise there is a huge community of ideologists actively building, buying, and working in the cryptocurrency world.
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] 

Bitcoin is a type of cryptocurrency: Balances are kept using public and private "keys," which are long strings of numbers and letters linked through the mathematical encryption algorithm that was used to create them. The public key (comparable to a bank account number) serves as the address which is published to the world and to which others may send bitcoins. The private key (comparable to an ATM PIN) is meant to be a guarded secret, and only used to authorize Bitcoin transmissions.

In May 2013, Ted Nelson speculated that Japanese mathematician Shinichi Mochizuki is Satoshi Nakamoto.[33] Later in 2013 the Israeli researchers Dorit Ron and Adi Shamir pointed to Silk Road-linked Ross William Ulbricht as the possible person behind the cover. The two researchers based their suspicion on an analysis of the network of bitcoin transactions.[34] These allegations were contested[35] and Ron and Shamir later retracted their claim.[36]
Unfortunately, these new highs for Bitcoin were so far from the past figures that the price was very volatile. The volatility was fueled by rumors of poor security on Mt. Gox exchange, which was part of about 70 percent of Bitcoin transactions of the time. This was likely a contributing factor in the drop of Bitcoin’s price from $1,230 on Dec. 4, 2013, to $750 by Dec. 7.
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To be accepted by the rest of the network, a new block must contain a so-called proof-of-work (PoW).[64] The system used is based on Adam Back's 1997 anti-spam scheme, Hashcash.[5][79] 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.[3]: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, ...[3]:ch. 8) before meeting the difficulty target.

In March the bitcoin transaction log called the blockchain temporarily split into two independent chains with differing rules on how transactions were accepted. For six hours two bitcoin networks operated at the same time, each with its own version of the transaction history. The core developers called for a temporary halt to transactions, sparking a sharp sell-off.[55] Normal operation was restored when the majority of the network downgraded to version 0.7 of the bitcoin software.[55] The Mt. Gox exchange briefly halted bitcoin deposits and the exchange rate briefly dipped by 23% to $37 as the event occurred[56][57] before recovering to previous level of approximately $48 in the following hours.[58] In the US, the Financial Crimes Enforcement Network (FinCEN) established regulatory guidelines for "decentralized virtual currencies" such as bitcoin, classifying American bitcoin miners who sell their generated bitcoins as Money Service Businesses (or MSBs), that may be subject to registration and other legal obligations.[59][60][61]
Bitcoin is a digital currency created in 2009. It follows the ideas set out in a white paper by the mysterious Satoshi Nakamoto, whose true identity has yet to be verified. Bitcoin offers the promise of lower transaction fees than traditional online payment mechanisms and is operated by a decentralized authority, unlike government-issued currencies.
If you are considering investing in cryptocurrencies, think of it like a trip to Vegas, self-made millionaire and best-selling author Tony Robbins suggests. In his own portfolio, Robbins directs a certain amount of money to risky ventures, but he doesn't rely on them to work out. For those investments, he said, "I know it is just for fun I'm investing, I know I could lose."
In late August 2012, an operation titled Bitcoin Savings and Trust was shut down by the owner, leaving around US$5.6 million in bitcoin-based debts; this led to allegations that the operation was a Ponzi scheme.[197][198][199][200] In September 2012, the U.S. Securities and Exchange Commission had reportedly started an investigation on the case.[201]
Satoshi's anonymity often raises unjustified concerns because of a misunderstanding of Bitcoin's open-source nature. Everyone has access to all of the source code all of the time and any developer can review or modify the software code. As such, the identity of Bitcoin's inventor is probably as relevant today as the identity of the person who invented paper.
Researchers have pointed out at a "trend towards centralization". Although bitcoin can be sent directly to the bitcoin network, in practice intermediaries are widely used.[30]:220–222 Bitcoin miners join large mining pools to minimize the variance of their income.[30]:215, 219–222[107]:3[108] Because transactions on the network are confirmed by miners, decentralization of the network requires that no single miner or mining pool obtains 51% of the hashing power, which would allow them to double-spend coins, prevent certain transactions from being verified and prevent other miners from earning income.[109] As of 2013 just six mining pools controlled 75% of overall bitcoin hashing power.[109] In 2014 mining pool obtained 51% hashing power which raised significant controversies about the safety of the network. The pool has voluntarily capped their hashing power at 39.99% and requested other pools to act responsibly for the benefit of the whole network.[110]

In 2013 and 2014, the European Banking Authority[144] and the Financial Industry Regulatory Authority (FINRA), a United States self-regulatory organization,[145] warned that investing in bitcoins carries significant risks. Forbes named bitcoin the best investment of 2013.[146] In 2014, Bloomberg named bitcoin one of its worst investments of the year.[147] In 2015, bitcoin topped Bloomberg's currency tables.[148]

This is a rather simple long term model.  And perhaps the biggest question it hinges on is how much adoption will bitcoin achieve?  Coming up with a value for the current price of bitcoin would involve pricing in the risk of low adoption or failure of bitcoin as a currency, which could include being displaced by one or more other digital currencies.  Models often consider the velocity of money, frequently arguing that since bitcoin can support transfers that take less than an hour, the velocity of money in the future bitcoin ecosystem will be higher than the current average velocity of money.  Another view on this though would be that velocity of money is not restricted by today's payment rails in any significant way and that its main determinant is the need or willingness of people to transact.  Therefore, the projected velocity of money could be treated as roughly equal to its current value.
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]