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Bitcoin’s hash puzzle is its proof-of-work: miners repeatedly hash a candidate block header until its double-SHA-256 result is no greater than the network’s target. It is a threshold search, not a riddle with a solution that can be derived. A lower target makes qualifying hashes rarer, so miners generally need more attempts.
What the hash puzzle asks miners to do
Each attempt uses a candidate block header. The hash function produces a 256-bit result that behaves unpredictably: miners cannot know in advance which input will produce a qualifying result, so they try different inputs. The proof is valid when the resulting hash, interpreted as a number, is less than or equal to Bitcoin’s current target.
The Bitcoin white paper describes the idea as searching for a value whose hash “begins with a number of zero bits.” That is an intuitive shorthand. The implemented validity check is a numerical comparison against a target threshold, not a test for a string of leading zero characters. See Bitcoin: A Peer-to-Peer Electronic Cash System and the developer documentation’s block chain reference.
What gets hashed
Miners hash the serialized block header, which is 80 bytes long. It includes the previous block’s hash, the Merkle root summarizing the block’s transactions, a timestamp, the difficulty target representation, and a nonce. The proof-of-work calculation applies SHA-256 twice to the header. The Bitcoin Developer Documentation describes the header fields and format.
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How miners search for a qualifying hash
- Build a candidate header. Mining software assembles header data for a proposed block, including the prior block reference and the Merkle root.
- Try a nonce. Mining hardware changes the header’s 32-bit nonce and computes the double-SHA-256 hash for each candidate.
- Compare with the target. If the hash is at or below the current target, the proof qualifies. If it is higher, the miner tries another candidate.
- Change more input when needed. Once the nonce range is exhausted, mining software can alter extra nonce data in the coinbase transaction. That changes the Merkle root, giving the miner a fresh set of header inputs to search.
Specialized mining hardware performs these repeated calculations. The puzzle’s difficulty is not a matter of finding a clever shortcut; the search relies on trying many possible inputs.
How difficulty and block timing relate
The target determines how many hash results qualify. A lower target means fewer qualifying results and more expected attempts. Bitcoin adjusts difficulty every 2,016 blocks, using timestamps to aim for 1,209,600 seconds—two weeks—for that span, as described in the Bitcoin Developer Guide.
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The protocol targets an average interval of 10 minutes per block, not a countdown that guarantees a block every 10 minutes. Because each hash attempt is probabilistic, an individual block can be found sooner or later. The Bitcoin.org mining FAQ explains the target average and how miners search for a valid block.
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Why the proof helps protect Bitcoin’s history
Every block refers to its predecessor through the previous block’s hash. If someone changes an earlier block, its contents—and therefore its proof-of-work hash—change. That breaks the link to the next block, and the altered block no longer has a valid proof under its original header. To make the rewritten history acceptable, the attacker would have to redo the work for the changed block and the blocks after it, then catch up with the continuing chain.
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Proof-of-work therefore makes rewriting history computationally expensive; it does not make it logically impossible. The effort required grows with the work that must be repeated and the blocks that must be caught up.
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