Bitcoin solves the "double spending problem" of electronic currencies (in which digital assets can easily be copied and re-used) through an ingenious combination of cryptography and economic incentives. In electronic fiat currencies, this function is fulfilled by banks, which gives them control over the traditional system. With bitcoin, the integrity of the transactions is maintained by a distributed and open network, owned by no-one.
At this point, the actual mining begins. In essence, each miner now tries to demonstrate to the rest of the network that his or her block of verified payments is the one true block, which will serve as the permanent record of those 2,000 or so transactions. Miners do this by, essentially, trying to be the first to guess their block’s numerical password. It’s analogous to trying to randomly guess someone’s computer password, except on a vastly larger scale. Carlson’s first mining computer, or “rig,” which he ran out of his basement north of Seattle, could make 12 billion “guesses” every second; today’s servers are more than a thousand times faster.
As noted in Nakamoto's whitepaper, it is possible to verify bitcoin payments without running a full network node (simplified payment verification, SPV). A user only needs a copy of the block headers of the longest chain, which are available by querying network nodes until it is apparent that the longest chain has been obtained. Then, get the Merkle branch linking the transaction to its block. Linking the transaction to a place in the chain demonstrates that a network node has accepted it, and blocks added after it further establish the confirmation.[2]
Lauren Miehe: The Prospector With a knack for turning old buildings into bitcoin mines, Miehe has helped numerous other outsiders set up mining operations in the basin and now manages sites for other miners. He’s been stunned by the interest in the region since bitcoin prices took off last year. “Right now, everyone is in full-greed mode,” he says. Here, Miehe works at his original mine, a half-megawatt operation a few miles from the Columbia River. | Patrick Cavan Brown for Politico Magazine
The amount of new bitcoin released with each mined block is called the block reward. The block reward is halved every 210,000 blocks, or roughly every 4 years. The block reward started at 50 in 2009, is now 12.5 in 2018, and will continue to decrease. This diminishing block reward will result in a total release of bitcoin that approaches 21 million.  
Bitcoin is in the very early stages of acceptance, and although it is already accepted as a means of payment by numerous merchants, it has yet to become more widely accepted and “mainstream.” This could change, however, as more and more users are attracted to cryptocurrencies for the various potential benefits they may provide. In fact, investors have been flocking to the currency in significant numbers, and some even feel that eventually Bitcoin and other cryptocurrencies could replace other traditional payment methods.

Bitcoin is in the very early stages of acceptance, and although it is already accepted as a means of payment by numerous merchants, it has yet to become more widely accepted and “mainstream.” This could change, however, as more and more users are attracted to cryptocurrencies for the various potential benefits they may provide. In fact, investors have been flocking to the currency in significant numbers, and some even feel that eventually Bitcoin and other cryptocurrencies could replace other traditional payment methods.


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 domain name "bitcoin.org" was registered on 18 August 2008.[15] In November 2008, a link to a paper authored by Satoshi Nakamoto titled Bitcoin: A Peer-to-Peer Electronic Cash System[5] was posted to a cryptography mailing list. Nakamoto implemented the bitcoin software as open source code and released it in January 2009.[16][17][10] Nakamoto's identity remains unknown.[9]
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