A Full Node first enforces consensus rules and only then selects the chain with the greatest cumulative work among valid chains. Miners compete to extend it. Agreement is not instantly final; Nakamoto consensus is later terminology that the whitepaper does not use.
The term combines Bitcoin's validation rules, block-producer selection through Proof of Work, fork choice and economic incentives. Reducing it to mining overlooks the Full Node that independently decides validity. [Satoshi Nakamoto — Bitcoin: A Peer-to-Peer Electronic Cash System] [The Bitcoin Backbone Protocol]
A Full Node checks transactions and blocks against its consensus rules. An invalid block remains invalid regardless of the work behind it; fork choice compares only valid candidates. Agreement assumes compatible rules among participants. [Satoshi Nakamoto — Bitcoin: A Peer-to-Peer Electronic Cash System] [Bitcoin Developer Guide — Block Chain] [Bitcoin Core v29.0 — Chainstate validation]
Proof of Work ties influence to computational work with energy and hardware costs rather than one vote per network identity. Creating many pseudonyms therefore does not by itself increase weight in chain selection. [Satoshi Nakamoto — Bitcoin: A Peer-to-Peer Electronic Cash System] [The Bitcoin Backbone Protocol]
Miners assemble candidate blocks and search for a header hash whose numerical value is less than or equal to the valid target. Competing valid blocks can appear simultaneously; propagation and subsequent work resolve the temporary fork under ordinary network conditions. [Satoshi Nakamoto — Bitcoin: A Peer-to-Peer Electronic Cash System] [Bitcoin Developer Guide — Block Chain]
A Full Node selects the valid branch with the greatest aggregate work, called chainwork. A block's work is derived from its target, not the number of attempts its miner actually performed. The longest chain thus means greatest work, not necessarily most blocks. [Satoshi Nakamoto — Bitcoin: A Peer-to-Peer Electronic Cash System] [Bitcoin Developer Guide — Block Chain] [Bitcoin Core v29.0 — Chainstate validation]
Assuming an honest majority of work and suitable block propagation, rewriting risk decreases with confirmation depth. An attacker must catch up with the competing chain. Confirmations are not mathematical irreversibility and do not protect against arbitrary attack models or victim isolation. [Satoshi Nakamoto — Bitcoin: A Peer-to-Peer Electronic Cash System] [The Bitcoin Backbone Protocol]
On mainnet the target is recalculated every 2016 blocks from past timestamps, aiming for a ten-minute average block interval. Adjustment moderates the long-term effect of hashrate changes; it guarantees neither exact individual intervals nor an immediate response to miners going offline. [Satoshi Nakamoto — Bitcoin: A Peer-to-Peer Electronic Cash System] [Bitcoin Developer Guide — Block Chain]
The block subsidy and fees reward extending accepted history. Majority hash power can reorganize valid blocks or censor transactions, but cannot make a Full Node accept an invalid signature, break issuance rules or spend others' funds without authorization. Attack risk also exists below 50%. [Satoshi Nakamoto — Bitcoin: A Peer-to-Peer Electronic Cash System] [Bitcoin Developer Guide — Block Chain] [Bitcoin Core v29.0 — Chainstate validation]
Safety and liveness depend on the adversarial work share, timely enough propagation and honest validation. Eclipse attacks and network partitions show why topology matters: a hashrate percentage alone is not a complete threat model. [The Bitcoin Backbone Protocol]
Classical BFT generally uses known participants and confirms by voting under explicit fault bounds and timing assumptions. Nakamoto consensus has open membership, work-based weight and probabilistic finality. It changes the model rather than merely implementing OM or PBFT. [The Bitcoin Backbone Protocol] [The Byzantine Generals Problem] [Bitcoin Optech — Consensus changes]
For the clearest picture, read this entry together with Bitcoin, Proof of Work, Difficulty adjustment, Consensus rules, Mining, Full Node. The reverse links also lead from Chain reorganization, Byzantine Generals Problem, Sybil attack, Selfish mining.