Ethereum's proof of work algorithm does not make use of Scrypt or Sha256, instead, it leverages EtHash, a Hashimoto / Dagger hybrid. You can read all about the theory behind this and its design in the Ethereum gitBook, mining chapter. Note that for Serenity (a future release, a major milestone on the Ethereum development roadmap) we are planning to switch to Proof of Stake (PoS).
I’d say Coinbase is the easiest way for newbies to buy Bitcoin because the site specifically caters to those who may not be all that familiar with cryptocurrencies. Admittedly, the fees are a little on the steep side compared to, say, LocalBitcoins and Kraken, but the good thing about using Coinbase is that you don’t have to worry too much about security.
HashFlare is a cloud mining service provided by HashCoins, a reputable crypto team that has been involved in blockchain since the inception of Bitcoin and has over 3 years of experience in cryptocurrency mining operations. HashFlare makes cryptocurrency mining accessible to anyone for an extremely low entrance point, meaning that anyone can try out a contract on a small scale to test the system. Furthermore, Mining is not the only way you can earn with HashFlare, you can also profit from an affiliate agreement.
Aside from the exchanges, you can also buy bitcoins on ebay and similar auction sites. Keep in mind that due to the possibility for chargebacks and fraud, bitcoin and other cryptocurrencies trade at a premium on ebay. Face to face meetups are another option to acquire bitcoins. Checklocalbitcoins.com for bitcoin sellers and buyers near your area. Always exercise caution when doing an offline exchange. Meet during the daytime and in places with a lot of people around. If possible, bring a friend.

Still, even supporters acknowledge that that glorious future is going to use a lot of electricity. It’s true that many of the more alarming claims—for example, that by 2020, bitcoin mining will consume “as much electricity as the entire world does today,” as the environmental website Grist recently suggested—are ridiculous: Even if the current bitcoin load grew a hundredfold, it would still represent less than 2 percent of total global power consumption. (And for comparison, even the high-end estimates of bitcoin’s total current power consumption are still less than 6 percent of the power consumed by the world’s banking sector.) But the fact remains that bitcoin takes an astonishing amount of power. By one estimate, the power now needed to mine a single coin would run the average household for 10 days.

What you may not know is the technology surrounding mining isn't just limited to consumer graphics cards. We’re beginning to see PC game platforms that allow you to mine when you’re away from your system, and exchange that digital currency for new games. There are even new Pokemon GO-style games hitting the app stores that are outdoor scavenger hunts with cryptocurrency as the ultimate treasure.
Luckily, the spread between the bid and the ask price is very low, most of the time ranging between 1 and 2 dollars. At a current bitcoin rate of $819, this amounts to an added cost of 0.1 to 0.25%. You only pay the spread if you want to enter a trade right away with a market order. If you placed a limit order to buy and you’re willing to wait until someone wants to sell, you can purchase your bitcoins at a small discount at the bid and later sell them at the ask, pocketing the spread in the process.

Binance Update: Binance offers $250,000 reward for details that lead to arrest of hackers. The China-based cryptocurrency exchange began live trading in July 2017, so is fairly new to the crypto exchange world. However it has proven itself thus far to its clients, with its robust charting software and both basic and advanced interfaces attracting novice and expert traders. We've written an in depth analysis of Binance

Bitcoin is taxable, whenever a taxable event occurs. A taxable event is whenever you cash out your bitcoin for any fiat currency (dollars, euros and etc.) or when you trade a bitcoin for anything (bartering). In taxation, bitcoin is best understood as an "asset." Whenever you hold an asset, it can increase or decrease in value. When you trade the bitcoin for fiat currency, then you're trading an asset for dollars. It works the same way as when you trade gold bullion for dollars.
Bitstamp has largely avoided the deposit and withdrawal problems that plague many bitcoin exchanges. With a lack of regulation on the upcoming virtual currency and its checkered past, many financial institutions remain reluctant to get involved with processing bitcoin related transactions.  You can deposit funds in USD, EUR, GBP and CHF. US clients are accepted.
Before you can find any blocks, however, your computer needs to go through a process called “building a DAG”. This DAG (short for “Directed Acyclic Graph”) is a large data structure (~1GB) required for mining, intended to prevent ASIC machines (“Application Specific Integrated Circuits”) from being mass manufactured for mining ether. Its goal is to protect miners like yourself so that you will only ever need your home computer to remain competitive. The DAG should take about 10 minutes to generate and as soon as it finishes, Geth will start mining automatically.
The user acknowledges and agrees that, to the fullest extent permitted by any applicable law, the disclaimers of liability contained herein apply to any and all damages or injury whatsoever caused by or related to risks of, use of, or inability to use, ethereum or the Ethereum platform under any cause or action whatsoever of any kind in any jurisdiction, including, without limitation, actions for breach of warranty, breach of contract or tort (including negligence) and that neither Stiftung Ethereum (i.e. Ethereum Foundation) nor Ethereum team shall be liable for any indirect, incidental, special, exemplary or consequential damages, including for loss of profits, goodwill or data that occurs as a result.
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