How do they find this number? By guessing at random. The hash function makes it impossible to predict what the output will be. So, miners guess the mystery number and apply the hash function to the combination of that guessed number and the data in the block. The resulting hash has to start with a pre-established number of zeroes. There's no way of knowing which number will work, because two consecutive integers will give wildly varying results. What's more, there may be several nonces that produce the desired result, or there may be none (in which case the miners keep trying, but with a different block configuration).
Bitmain acquired this mining facility in Inner Mongolia a couple years ago and has turned it into one of the most powerful money factories on the Bitcoin network. It quite literally metabolizes electricity into money. By my own calculations, the hardware on the grounds—some 21,000 computers—accounted for about 4 percent of all the computing power in the Bitcoin network when I visited.
Controlling and monitoring your mining rig requires dedicated software. Depending on what mining rig you have, you’ll need to find the right software. Many mining pools have their own software, but some don’t. In case you’re not sure which mining software you need, you can find a list of Bitcoin mining software here. Also, if you want to compare different mining software, you can do it here.

Bitcoin mining is the processing of transactions on the Bitcoin network and securing them into the blockchain. Each set of transactions that are processed is a block. The block is secured by the miners. Miners do this by creating a hash that is created from the transactions in the block. This cryptographic hash is then added to the block. The next block of transactions will look to the previous block’s hash to verify it is legitimate. Then your miner will attempt to create a new block that contains current transactions and new hash before anyone else’s miner can do so.

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.[8]
Despite having similar needs, there is a good deal of diversity in how chip designers build their hashing engines, says Hanke, who also served as the chief technology officer of a now-defunct mining rig manufacturer called CoinTerra. For example, Bitmain uses pipelining—a strategy that links the steps in a process into a chain in which the output of one step is the input of the next. Bitmain competitor BitFury has chosen not to use that technology.

Generally speaking, every bitcoin miner has a copy of the entire block chain on her computer. If she shuts her computer down and stops mining for a while, when she starts back up, her machine will send a message to other miners requesting the blocks that were created in her absence. No one person or computer has responsibility for these block chain updates; no miner has special status. The updates, like the authentication of new blocks, are provided by the network of bitcoin miners at large.
Several news outlets have asserted that the popularity of bitcoins hinges on the ability to use them to purchase illegal goods.[128][224] Nobel-prize winning economist Joseph Stiglitz says that bitcoin's anonymity encourages money laundering and other crimes, "If you open up a hole like bitcoin, then all the nefarious activity will go through that hole, and no government can allow that." He's also said that if "you regulate it so you couldn’t engage in money laundering and all these other [crimes], there will be no demand for Bitcoin. By regulating the abuses, you are going to regulate it out of existence. It exists because of the abuses."[225][226]
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Bitcoin mining is the process by which the transaction information distributed within the Bitcoin network is validated and stored on the blockchain. Bitcoin mining serves to both add transactions to the block chain and to release new Bitcoin. The concept of Bitcoin mining is simply the process of generating additional Bitcoins until the supply cap of 21 million coins has been reached.  What makes the validation process for Bitcoin different from traditional electronic payment networks is the absence of middle man in the architecture. The process of validating transactions and committing them to the blockchain involves solving a series of specialized math puzzles. In the process of adding transactions to the network and securing them into the blockchain, each set of transactions that are processed is called block, and multiple chains of blocks is referred to as the blockchain.
In March 2013 the blockchain temporarily split into two independent chains with different rules. The two blockchains operated simultaneously for six hours, each with its own version of the transaction history. Normal operation was restored when the majority of the network downgraded to version 0.7 of the bitcoin software.[36] The Mt. Gox exchange briefly halted bitcoin deposits and the price dropped by 23% to $37[37][38] before recovering to previous level of approximately $48 in the following hours.[39] The US 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 (MSBs), that are subject to registration or other legal obligations.[40][41][42] In April, exchanges BitInstant and Mt. Gox experienced processing delays due to insufficient capacity[43] resulting in the bitcoin price dropping from $266 to $76 before returning to $160 within six hours.[44] The bitcoin price rose to $259 on 10 April, but then crashed by 83% to $45 over the next three days.[34] On 15 May 2013, US authorities seized accounts associated with Mt. Gox after discovering it had not registered as a money transmitter with FinCEN in the US.[45][46] On 23 June 2013, the US Drug Enforcement Administration (DEA) listed 11.02 bitcoins as a seized asset in a United States Department of Justice seizure notice pursuant to 21 U.S.C. § 881.[47] This marked the first time a government agency had seized bitcoin.[48][49] The FBI seized about 26,000 bitcoins in October 2013 from the dark web website Silk Road during the arrest of Ross William Ulbricht.[50][51][52] Bitcoin's price rose to $755 on 19 November and crashed by 50% to $378 the same day. On 30 November 2013 the price reached $1,163 before starting a long-term crash, declining by 87% to $152 in January 2015.[34] On 5 December 2013, the People's Bank of China prohibited Chinese financial institutions from using bitcoins.[53] After the announcement, the value of bitcoins dropped,[54] and Baidu no longer accepted bitcoins for certain services.[55] Buying real-world goods with any virtual currency had been illegal in China since at least 2009.[56]