How hard are the puzzles involved in mining? Well, that depends on how much effort is being put into mining across the network. The difficulty of the mining can be adjusted, and is adjusted by the protocol every 2016 blocks, or roughly every 2 weeks. The difficulty adjusts itself with the aim of keeping the rate of block discovery constant. Thus if more computational power is employed in mining, then the difficulty will adjust upwards to make mining harder.  And if computational power is taken off of the network, the opposite happens. The difficulty adjusts downward to make mining easier.

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.
What bitcoin miners actually do could be better described as competitive bookkeeping. Miners build and maintain a gigantic public ledger containing a record of every bitcoin transaction in history. Every time somebody wants to send bitcoins to somebody else, the transfer has to be validated by miners: They check the ledger to make sure the sender isn’t transferring money she doesn’t have. If the transfer checks out, miners add it to the ledger. Finally, to protect that ledger from getting hacked, miners seal it behind layers and layers of computational work—too much for a would-be fraudster to possibly complete.
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.
Benny: The Rogue Miner “Benny,” a self-taught, 20-something computer whiz, set up three mining servers in his Wenatchee home last summer. Since then he has made enough profit not only to recover his initial investment but also to pay his monthly mortgage. As a bonus, the heat from the computers keeps his home heated all winter. “It’s just basically free money,” says Benny, pictured here with his homemade mining operation. | Patrick Cavan Brown for Politico Magazine
Bitcoin is the world’s first cryptocurrency. It is a purely peer-to-peer electronic cash system that allows online payments to be sent directly from one party to another without going through a financial institution. The Bitcoin system is the most widely accepted cryptocurrency system at present. However, due to its initial setting, such as block size and block time, its performance is limited to less than 10 transactions per second.

Bitcoin is an increasingly popular cryptocurrency that utilizes blockchain technology to facilitate transactions. Basically, a user obtains a Bitcoin wallet that can be used for storing bitcoins and both sending and receiving of payments. The blockchain technology used by Bitcoin is really just a shared public ledger that is used by the entire public network. The technology used is secured through cryptography, a branch of mathematics that provides a highly secure means of facilitating and recording transactions on the network.
Nobody owns the Bitcoin network much like no one owns the technology behind email or the Internet. Bitcoin transactions are verified by Bitcoin miners which has an entire industry and Bitcoin cloud mining options. While developers are improving the software they cannot force a change in the Bitcoin protocol because all users are free to choose what software and version they use.

Requiring a proof of work to accept a new block to the blockchain was Satoshi Nakamoto's key innovation. The mining process involves identifying a block that, when hashed twice with SHA-256, yields a number smaller than the given difficulty target. While the average work required increases in inverse proportion to the difficulty target, a hash can always be verified by executing a single round of double SHA-256.
Electrum gets high marks for its ease of use and user interface, which is always nice, but the real reason it's the best bitcoin wallet for desktop is its safety and reliability. Like any desktop wallet that's worth its salt, users get to control their private key; Electrum doesn't know what it is. Since your private key, a long string of letters and numbers, gives you access to your bitcoin, you need to keep that, you know, private.
Let’s say a hacker wanted to change a transaction that happened 60 minutes, or six blocks, ago—maybe to remove evidence that she had spent some bitcoins, so she could spend them again. Her first step would be to go in and change the record for that transaction. Then, because she had modified the block, she would have to solve a new proof-of-work problem—find a new nonce—and do all of that computational work, all over again. (Again, due to the unpredictable nature of hash functions, making the slightest change to the original block means starting the proof of work from scratch.) From there, she’d have to start building an alternative chain going forward, solving a new proof-of-work problem for each block until she caught up with the present.
Before you read further, please understand that most bitcoin users don't mine! But if you do then this Bitcoin miner is probably the best deal. Bitcoin mining for profit is very competitive and volatility in the Bitcoin price makes it difficult to realize monetary gains without also speculating on the price. Mining makes sense if you plan to do it for fun, to learn or to support the security of Bitcoin and do not care if you make a profit. If you have access to large amounts of cheap electricity and the ability to manage a large installation and business, you can mine for a profit.
As more and more miners competed for the limited supply of blocks, individuals found that they were working for months without finding a block and receiving any reward for their mining efforts. This made mining something of a gamble. To address the variance in their income miners started organizing themselves into pools so that they could share rewards more evenly. See Pooled mining and Comparison of mining pools.
The overwhelming majority of bitcoin transactions take place on a cryptocurrency exchange, rather than being used in transactions with merchants.[133] Delays processing payments through the blockchain of about ten minutes make bitcoin use very difficult in a retail setting. Prices are not usually quoted in units of bitcoin and many trades involve one, or sometimes two, conversions into conventional currencies.[30] Merchants that do accept bitcoin payments may use payment service providers to perform the conversions.[134]
In January 2009, the bitcoin network was created when Nakamoto mined the first block of the chain, known as the genesis block.[18][19] Embedded in the coinbase of this block was the following text: "The Times 03/Jan/2009 Chancellor on brink of second bailout for banks."[10] This note has been interpreted as both a timestamp and a comment on the instability caused by fractional-reserve banking.[20]:18