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).

Bitcoin's price is also quite dependent on the size of its mining network, since the larger the network is, the more difficult – and thus more costly – it is to produce new bitcoins. As a result, the price of bitcoin has to increase as its cost of production also rises. The Bitcoin mining network's aggregate power has more than tripled over the past twelve months.

Backtracking a bit, let's talk about "nodes." A node is a powerful computer that runs the bitcoin software and helps to keep bitcoin running by participating in the relay of information. Anyone can run a node, you just download the bitcoin software (free) and leave a certain port open (the drawback is that it consumes energy and storage space – the network at time of writing takes up about 145GB). Nodes spread bitcoin transactions around the network. One node will send information to a few nodes that it knows, who will relay the information to nodes that they know, etc. That way it ends up getting around the whole network pretty quickly.
The first post was made on 31 August and suggested that the funds may be connected to the now-defunct dark web market Silk Road which handled the trade of billions of dollars worth of contraband such as recreational and prescription drugs, illegal weapons and pornography, malware, hacking services, guides to various types of criminal activity, and other black market goods and services.
The primary purpose of mining is to allow Bitcoin nodes to reach a secure, tamper-resistant consensus. Mining is also the mechanism used to introduce bitcoins into the system. Miners are paid transaction fees as well as a subsidy of newly created coins, called block rewards. This both serves the purpose of disseminating new coins in a decentralized manner as well as motivating people to provide security for the system through mining.
A “wallet” is basically the Bitcoin equivalent of a bank account. It allows you to receive bitcoins, store them, then send them to others. There are two main types of wallets, software and web. A software wallet is one that you install on your own computer or mobile device. You are in complete control over the security of your coins, but such wallets can sometimes be tricky to install and maintain.A web wallet, or hosted wallet, is one that is hosted by a third party. These are often much easier to use, but you have to trust the provider (host) to maintain high levels of security to protect your coins.
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).

Nakamoto is estimated to have mined one million bitcoins[26] 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.[27][28] Andresen then sought to decentralize control. This left opportunity for controversy to develop over the future development path of bitcoin.[29][28]

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