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Why Are Shares Considered “Proof-of-Work” Even Though They Don’t Solve the Block?

Shares are considered proof-of-work because they demonstrate that the miner has performed the necessary computational effort (hashing) to find a hash below the pool's set difficulty target. This process is identical to finding a block, only the difficulty threshold is lower.

The pool accepts this as verifiable evidence of the miner's contribution to the collective effort.

How Does a Proof-of-Work Consensus Mechanism Utilize Hashing?
How Does the Pool Difficulty Setting Relate to the Network Difficulty?
How Does the “Hashing” Process Relate to Bitcoin’s Proof-of-Work?
How Does Hashing Secure the Creation of a New Block in a Proof-of-Work System?