Prime Mining as Cooperative Proof-of-Work:

We present a blockchain architecture in which the fundamental proof-of-work consists of advancing the frontier of known primes in the integers. A block is valid only if it contains the next unused rational prime and certifies that all intervening integers are composite. Unlike hash-based proof-of-work, mining becomes a cooperative process: miners receive proportional rewards for contributing composite factorizations, while the prime discoverer receives the primary reward. This mechanism embodies Nashian cooperative equilibrium, ensuring that honest participation strictly dominates strategic deviation. Wallets maintain fractional ownership of each prime through a vector representation synchronized with an integer divisibility encoding. The resulting ledger features deterministic asset issuance, unique non-fungible prime assets, and immediate finality. We also describe optional extension chains defined over algebraic integer rings, enabling more complex forms of mathematical proof-of-work without altering the main chain.

A decentralized digital currency requires a publicly verifiable mechanism for assigning value, recording ownership, and preventing double spending without trusted intermediaries. Bitcoin achieves this using a uniform currency unit and a competitive hash-based proof-of-work system in which miners race to solve useless puzzles. While effective, Bitcoin’s design rewards winner-takes-all competition, concentrates mining power, and discards nearly all computational work. This paper introduces a cryptocurrency built instead on constructive number-theoretic work and Nashian cooperative mining incentives. In this system, value arises from the mathematical structure of the prime numbers. Each prime—once discovered by proof-of-work—forms a unique and indivisible asset class. Instead of competing solely for a single reward, miners contribute collaboratively to certifying the integer interval leading to each newly discovered prime. Rewards are divided proportionally among contributors in ways that mirror John Nash’s principles of stable cooperative equilibria: each participant receives a share commensurate with their demonstrable contribution, and no miner can improve their expected outcome by deviating from honest behavior. Please read the full white paper at https://midlincoln.com/pdfs/primenumberblockchain.pdf