Primecoin: Cryptocurrency with Prime Number Proof-of-Work
📜 Abstract
A new type of proof-of-work based on searching for prime numbers is introduced in peer-to-peer cryptocurrency designs. Three types of prime chains known as Cunningham chain of first kind, Cunningham chain of second kind and bi-twin chain are qualified as proof-of-work. Prime chain is linked to block hash to preserve the security property of Nakamoto’s Bitcoin, while a continuous difficulty evaluation scheme is designed to allow prime chain to act as adjustable-difficulty proof-of-work in a Bitcoin like cryptocurrency.
✨ Summary
Summary
The paper introduces Primecoin, a cryptocurrency whose proof-of-work is based on discovering Cunningham chains and bi-twin chains of prime numbers rather than repeatedly hashing arbitrary data. It describes how these chains can be verified efficiently using probable-primality tests, while imposing bounds on prime size so that verification remains practical for network nodes.
The design links each prime-chain origin to the block-header hash, making the proof specific to a block and preventing straightforward reuse. It also proposes a fractional chain-length measure based on the Fermat-test remainder, allowing mining difficulty to be adjusted continuously while retaining a Bitcoin-like chain-selection model. The paper discusses the resulting security limitations, particularly the possibility that the non-linear difficulty model could slightly weaken the usual majority-hash-power assumption.
Primecoin was subsequently implemented as an operating cryptocurrency and open-source software project. The project describes its protocol as introducing scientific-computing proof-of-work to cryptocurrency technology. (github.com) Later work on proof-of-useful-work treats Primecoin as an early and successful example of replacing conventional hash-based mining with computational work having an external mathematical objective. (arxiv.org) Subsequent proof-of-useful-work research, including Coin.AI, cites Primecoin as a precedent while exploring alternative workloads such as distributed deep-learning computation. (mdpi.com) The available references therefore indicate influence primarily as a demonstrative cryptocurrency implementation and as a conceptual precursor to later proof-of-useful-work research, rather than evidence of broad adoption as a dominant cryptocurrency-mining design.