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Definition: proof-of-work algorithm

A blockchain consensus mechanism that requires a miner to solve a mathematical puzzle. Bitcoin uses the proof-of-work (PoW) method, as well as Ethereum prior to Version 2.0. See Ethereum 2.0, consensus mechanism and cryptographic hash function.

As a total aside from crypto, in order to impede spammers, a variation of the PoW method has been proposed for email. For example, if every message had to wait just 15 seconds before being sent, a compromised computer could never be used to unleash tens of thousands of messages.

For Cryptocurrencies
A very controversial subject in the crypto world, proof-of-work uses massive amounts of electricity. See Bitcoin and Bitcoin mining.

How PoW Works
A challenge string is presented that has to be hashed together with an unknown number to derive a result that matches some criterion such as the first 20 bits must be zero. When that is reached, it proves that a certain amount of computer processing was undertaken. It takes an enormous number of calculations to find a number that proves the challenge, and miner hardware is rated in "hashes per second" (see hash rate, miner hardware and cryptographic hash function).

Proof-of-Stake (PoS) Algorithm
In contrast, the proof-of-stake (PoS) method differs entirely. PoS miners compete to confirm transactions based on how much crypto they have locked up and held ("staked") for this purpose. From a mathematical standpoint, proof-of-stake is much less complicated than proof-of-work, and proof-of-stake uses considerably less electricity.

For example, next to Bitcoin, Ethereum is an extremely popular blockchain that has used proof-of-work since its launch in 2015. However, Ethereum 2.0 is a proof-of-stake method that is being tested to replace the PoW algorithm (see Ethereum 2.0). Why change? Because as proof-of-work (PoW) miners become more monopolistic, any single miner with 51% or more of the network's computing power could invalidate good transactions and double spend the coins. With proof-of-stake (PoS), any miner with that much "at stake" would not want to destabilize the system. See Ethereum.