Proof of work is a way of making a claim expensive to produce and cheap to check. In Bitcoin, a miner must find a block header whose double SHA-256 hash falls below a numeric target. Finding one takes an enormous number of attempts; verifying one takes a single hash. Any node can confirm in microseconds that a block cost real work to produce.
That asymmetry solves a specific problem: how a network of anonymous participants agrees on one transaction history when anyone can join and nobody is in charge. The rule is that the valid chain is the one with the most cumulative work, and cumulative work is something an observer can measure independently rather than take on trust.
The mechanics
The hash function is SHA-256 applied twice. Its relevant property is that the output is unpredictable from the input and uniformly distributed, so there is no way to reason toward a valid nonce. Searching is the only strategy, and every attempt is independent of every previous one.
The block header contains six fields: the version, the previous block's hash, the merkle root of the block's transactions, a timestamp, the target in compressed form known as bits, and the nonce. Miners iterate the nonce, and when its roughly 4.3 billion values are exhausted they change an extra field in the coinbase transaction, which changes the merkle root and opens a fresh search space.
The previous block's hash is what chains blocks together. Changing any transaction in a historical block changes that block's hash, which invalidates every block after it. Rewriting history therefore means redoing the work for every subsequent block while the honest network extends the real chain, which is the security property in one sentence.
Target and difficulty
The target is the threshold a block hash must fall below. Difficulty is a more readable expression of the same thing: the ratio between the maximum permitted target and the current target. A difficulty of 127.45 trillion, roughly where Bitcoin sat on 8 September 2026, means blocks are about 127.45 trillion times harder to find than at the easiest setting the protocol allows.
Retargeting happens every 2,016 blocks. The network compares how long those blocks actually took against the 20,160 minutes they should have taken and scales the target accordingly, with the adjustment clamped so difficulty cannot change by more than a factor of four in a single retarget. The clamp prevents a sudden hashrate collapse or spike from destabilizing block production.
| Concept | Definition | Direction |
|---|---|---|
| Target | The numeric threshold a block hash must fall below | Lower target means harder |
| Difficulty | Maximum target divided by current target | Higher difficulty means harder |
| Retarget interval | Every 2,016 blocks, about two weeks | Fixed by protocol |
| Adjustment limit | Factor of four up or down | Fixed by protocol |
Why the cost being external matters
The security argument for proof of work turns on where an attacker's cost comes from. To attack a proof-of-work chain, an attacker must acquire hardware and buy electricity. Both are external to the network. The protocol cannot confiscate them, and a failed attack still leaves the electricity spent and the hardware bought.
Proof of stake makes the cost internal. Validators post the network's own token as collateral, and misbehavior can be punished by destroying that collateral, a mechanism called slashing, which has no proof-of-work equivalent. The tradeoff is that the security budget is denominated in the asset being secured, so it falls with the token's price, and a new node cannot verify the chain from genesis by measuring accumulated cost alone. It needs a recent trusted checkpoint, a requirement known as weak subjectivity.
Neither model is strictly better. Proof of work buys objectivity and externally denominated security at the cost of ongoing energy consumption. Proof of stake buys energy efficiency and punishable misbehavior at the cost of a security budget tied to its own token and a dependence on checkpoints.
What a 51 percent attack actually does
An attacker with a majority of hashrate can reorder or exclude recent transactions and spend the same coins twice by broadcasting a payment, waiting for it to confirm, then publishing a longer chain in which it never happened. What such an attacker cannot do is spend coins they do not own, change the issuance schedule, or alter transactions buried under substantial work.
Smaller chains have been attacked repeatedly, generally by renting hashrate rather than buying hardware. Bitcoin Gold lost roughly $18 million to double spends across several exchanges in May 2018. Ethereum Classic lost about 219,500 ETC, then worth roughly $1.1 million, in January 2019, and was attacked again in 2020. Vertcoin and Verge suffered smaller incidents.
Selfish mining and other theoretical attacks
Majority attacks are not the only ones described in the literature. Selfish mining is a strategy in which a miner who finds a block withholds it, continues mining privately, and releases the longer private chain later, wasting the honest network's effort. Analysis published in 2013 argued the strategy could be profitable with less than half the network's hashrate under some assumptions about how quickly blocks propagate.
No sustained selfish mining has been observed on Bitcoin. The reasons offered include that the strategy is detectable, that a large miner has a substantial investment in the network's credibility, and that the propagation assumptions the analysis requires do not hold well in practice. The theoretical result stands; its practical relevance remains contested.
The energy question
Proof of work consumes electricity by design, and the amount is substantial. Published estimates of Bitcoin's annual consumption differ significantly between research groups because they disagree about how to infer the hardware mix from observable hashrate and about which energy sources to attribute. Estimates of the share supplied by low-carbon generation vary even more widely, and are frequently cited without the methodology attached.
The defensible position is that consumption is large, that precise figures carry real uncertainty, and that the substantive argument is about whether the energy buys something worth its cost. Anyone presenting a single number as settled fact is overstating what the evidence supports.