Nakamoto consensus: the most-work chain

Wonder

1. How can thousands of strangers agree on a single history without a leader or a vote?
2. Why does adding one more block make an old transaction harder to reverse?
3. What happens when two chains exist simultaneously for ten minutes?

Explore

1. Consensus in Bitcoin is not an election. There is no fixed membership, no leader, and no formal vote. Every full node independently verifies transactions against a comprehensive set of rules. When miners aggregate these valid transactions into blocks, they perform proof-of-work: solving a computationally expensive puzzle that serves as a timestamp. This work anchors the block to the chain, making it part of a global history that is costly to alter.
2. When two competing chains appear, every node follows a simple rule: adopt the chain with the most cumulative proof-of-work. When one branch pulls ahead in accumulated work, the other is abandoned, and its transactions return to the mempool unless the winning branch already contains them. This mechanism neutralizes Sybil attacks; creating thousands of fake identities is useless if the holder lacks proportional computational power. Weight, measured in proof of work, decides which valid history wins, not identity.
3. Agreement is probabilistic, not absolute. A transaction becomes more secure with each block added on top of it because an attacker must redo the work for that block and every subsequent one to overtake the honest chain. Section 11 of the whitepaper calculates this risk: if an attacker controls a share q of hashpower, the probability of them ever catching up from z blocks behind drops exponentially as z increases.
4. For an attacker with only 10% of the network’s hashrate (q = 0.1), the chance of reversing a transaction buried under five confirmations is less than 0.1%. This mathematical decay provides the security model for merchants and exchanges. Short reorganizations, where a few blocks are discarded in favor of another valid chain, are part of normal operation and do not indicate failure but rather the dynamic competition inherent in proof-of-work.
5. Section 6 argues that incentives align rational actors with network stability. A miner holding significant hashpower earns more by following the rules than by attacking the system, because the value of their coins depends on the network’s trustworthiness. Destroying that trust would devalue the very assets they hold. This economic coupling ensures that large players have a vested interest in maintaining consensus rather than disrupting it.
6. Reproduce the whitepaper’s arithmetic. Section 11 gives a short C program and a table: for an attacker with q = 0.1, the chance of catching up from five blocks behind is about 0.0009, under 0.1%. For q = 0.3 the same five blocks still leave about an 18% chance, and it takes far deeper confirmation to push the risk below 0.1%. Security depends on how much hashpower an attacker could muster, not on a fixed number of blocks.

Key facts

Exercise nine, six, three, one

Fact check

Dates, figures and claims checked against the published sources listed below.

• S. Nakamoto, 'Bitcoin: A Peer-to-Peer Electronic Cash System' (2008), Sections 4, 6, and 11.
• J. Garay, A. Kiayias & N. Leonardos, 'The Bitcoin Backbone Protocol: Analysis and Applications' (2015)