FACTOR is a decentralized infrastructure protocol that rewards real mathematical problem solving through Useful Proof of Work (uPoW). It transforms cryptographic mining into an open marketplace for integer factorization, accessible to researchers, miners, developers, and institutions that want to advance applied mathematics and computational cryptography. Unlike traditional Proof of Work networks such as Bitcoin, where energy is spent on arbitrary hashing to secure the chain, FACTOR redirects that same computational effort toward solving meaningful mathematical challenges. Every cycle of computation contributes to the factorization of large composite numbers, the foundation of modern encryption systems. This approach preserves the security and fairness of decentralized mining while channeling it into a task with direct academic, industrial, and cryptographic value. At its core, FACTOR merges blockchain incentives with scientific utility. The protocol introduces an on-chain bounty marketplace, allowing anyone to post mathematical or cryptographic challenges and reward the community for solving them. Researchers can outsource difficult factorizations. Miners can compete to solve them. Developers can build tools and analytics around them. The result is a self-sustaining ecosystem that connects decentralized finance, cybersecurity, and high-performance computing. FACTOR’s architecture is built around three main pillars: The Factory – the mining layer where useful computations occur and proofs are submitted. Gateway – the bridge between research institutions, enterprises, and the network’s computational layer. KeyBoard – the interface for posting and managing bounties, publishing results, and coordinating verifiable proofs. This structure ensures scalability, anonymity, and interoperability across disciplines and applications. Beyond the technology, FACTOR represents a philosophical shift in blockchain design. It challenges the idea that mining must be wasteful by turning Proof of Work into a public good. Every solved factorization contributes to both the network’s consensus and the advancement of knowledge in mathematics and cryptography. In essence, FACTOR is not just another coin or chain. It is a foundation for crypto-incentivized computation where the act of securing a ledger becomes inseparable from performing valuable scientific work. By merging incentive mechanics with real-world utility, FACTOR redefines decentralized computing as a marketplace for knowledge, not waste.