BA-08 · LESSON 02

Proof of work

KEY DEFINITIONS

Terms used in this lesson

Proof-of-work target: The maximum header-hash value accepted for a block; lowering it makes valid hashes harder to find.
Hash rate: The number of mining hash attempts performed per second.
SHA-256: A cryptographic hash function used throughout Bitcoin to produce fixed-size 256-bit digests.

Mining searches header variations for a hash below the target, making history costly to extend and rewrite.

45 min Difficulty 2/5 Not started

VISUAL MODEL

See the whole mechanism before going step by step

Use the diagrams to orient yourself. Then the guided explanation below teaches every part in depth.

4 explanatory views

CONCEPT-SPECIFIC MAP · pow targetProof of work is a numeric comparisonSelect any state to inspect its exact role.

RELATIONSHIP MAPOrdered mechanism flow

01
HEADERGenesis nonce 2083236893
A miner varies nonce and other candidate data to obtain another header.
02
HASH256000000000019d668...
Double-SHA256 behaves like an unpredictable draw for each changed header.
03
TARGET00000000ffff0000...
Genesis nBits 0x1d00ffff expands to this 256-bit threshold.
04
COMPAREHash <= target
The comparison is exact; leading zeros are only a visual consequence of a small hash value.
05
RESULTAccept proof of work
Nodes perform the check cheaply even though finding a passing header required repeated trials.

Rule shown: Interpret the header hash as a 256-bit number and accept only when it is less than or equal to the target encoded by nBits.

STAGE 1 OF 5HEADER: Genesis nonce 2083236893

A miner varies nonce and other candidate data to obtain another header.

Governing relationship: Interpret the header hash as a 256-bit number and accept only when it is less than or equal to the target encoded by nBits. Complete path: 1. HEADER, Genesis nonce 2083236893. A miner varies nonce and other candidate data to obtain another header. 2. HASH256, 000000000019d668.... Double-SHA256 behaves like an unpredictable draw for each changed header. 3. TARGET, 00000000ffff0000.... Genesis nBits 0x1d00ffff expands to this 256-bit threshold. 4. COMPARE, Hash <= target. The comparison is exact; leading zeros are only a visual consequence of a small hash value. 5. RESULT, Accept proof of work. Nodes perform the check cheaply even though finding a passing header required repeated trials.

1. State transitionWhat exists, what changes, and what results

BEFORE

Toy hashes range from 0 to 255 and target is 15.

MECHANISM

The header stores a compact representation called nBits. Nodes decode it and reject invalid or out-of-range targets.

AFTER

Difficulty changes probability, not a miner's ability to predict which nonce will work.

Text equivalent: Starting from Toy hashes range from 0 to 255 and target is 15. The mechanism begins when The header stores a compact representation called nBits. Nodes decode it and reject invalid or out-of-range targets. The resulting lesson is Difficulty changes probability, not a miner's ability to predict which nonce will work.

2. Mechanism pathSelect a stage to inspect its job

STAGE 1 OF 5

Decode the target

The header stores a compact representation called nBits. Nodes decode it and reject invalid or out-of-range targets.

Complete path: 1. Decode the target: The header stores a compact representation called nBits. Nodes decode it and reject invalid or out-of-range targets. 2. Hash one header: The miner double-hashes exactly 80 header bytes. SHA-256 output behaves unpredictably enough that each changed header is another trial. 3. Compare numeric values: Interpreted under the consensus convention, the hash passes only when it is no greater than target. 4. Repeat with new candidates: Miners vary header-connected data and search enormous numbers of candidates. Expected work is proportional to 2^256 divided by the target range. 5. Verify cheaply: Any node hashes the announced header once and compares it with the target, making verification far cheaper than the search.

3. Rule and failure boundaryWhat accepts the result and where it can stop

ACCEPTED PATH

In the displayed finite space, qualifying outcomes are counted inclusively from zero through target, so probability is qualifying outcomes divided by all outcomes.

CHANGED CONDITION

A target-plus-one hash fails, and prior failed trials do not improve the next independent hash probability.

Important distinction: Miners solve increasingly complex mathematical equations as they approach a block. They repeatedly hash different headers. Previous failures do not move one candidate closer to success; each trial is another probabilistic search.

Text equivalent: The accepted path is enforced by In the displayed finite space, qualifying outcomes are counted inclusively from zero through target, so probability is qualifying outcomes divided by all outcomes. If the required condition changes, A target-plus-one hash fails, and prior failed trials do not improve the next independent hash probability.

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Learn the idea

Proof of work requires the numeric double-SHA-256 block-header hash to be less than or equal to a target. A lower target is harder because fewer of the 2^256 possible hash values qualify. Hash rate measures attempted hashes per second; it changes expected discovery time, not any individual hash's uniform probability.

GUIDED EXPLANATION1/5 ideas inspected

Decode the target

The header stores a compact representation called nBits. Nodes decode it and reject invalid or out-of-range targets.

The worked example follows the explanation

Inspect every idea above to open it.

Important distinction“Miners solve increasingly complex mathematical equations as they approach a block.”

They repeatedly hash different headers. Previous failures do not move one candidate closer to success; each trial is another probabilistic search.

FINISH LEARNING FIRST

The questions unlock after every required learning activity

Inspect every guided idea, open the worked example, rebuild its mechanism, and complete the deterministic lesson tool. Your progress is saved automatically.