The Mersenne Chain Reactor: A Physical Saturation Law for Mersenne Primes

The Mersenne Chain Reactor: A Physical Saturation Law for Mersenne Primes | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Physical Sciences - Article The Mersenne Chain Reactor: A Physical Saturation Law for Mersenne Primes Moustafa Ibrahim, Belal Ibrahim, Rawan Ibrahim This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8876072/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract The search for Mersenne primes at astronomical scales has reached a physical bottleneck: as numbers grow, the energy and time required for arithmetic verification become prohibitive on classical processors. Here we report a fundamental paradigm shift in the physics of computation and information. We introduce the Mersenne Chain Reactor (MCR), a physical system that determines the primality of Mersenne numbers without performing arithmetic operations. The reactor does not add, subtract, multiply, divide, or execute iterative numerical steps. Instead, primality is decided through a physical propagation process. By encoding the problem into a cyclic lattice and injecting a signal—optical, electrical, or quantum—the MCR transforms primality testing into a physical experiment. If the signal propagates and saturates the entire structure, the corresponding Mersenne number is prime; if destructive interference leaves persistent voids, it is composite. Crucially, the verdict is reached not by iterative computation, but by the completion of a single physical propagation event. The total latency is therefore bounded by the signal time-of-flight across the reactor geometry, yielding a constant physical depth independent of arithmetic complexity. In this sense, the MCR functions not as a calculator, but as an observational instrument—much as a balance does not compute weight, nor a thermometer compute temperature. We propose this architecture as a new experimental lens on the deep structure of prime numbers and a decisive shift from arithmetic computation to physical judgement. Physical sciences/Physics/Information theory and computation Physical sciences/Mathematics and computing/Information technology Physical sciences/Engineering/Electrical and electronic engineering Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Thermodynamics Full Text Additional Declarations The authors declare potential competing interests as follows: The authors declare that a U.S. Provisional Patent Application (No. 63/981,494) has been filed regarding the Mersenne Chain Reactor technology described in this work. Supplementary Files MersenneChainReactorNatureSI.pdf Supplementary Information Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Here we report a fundamental paradigm shift in the physics of computation and information.\r\n\r\nWe introduce the Mersenne Chain Reactor (MCR), a physical system that determines the primality of Mersenne numbers without performing arithmetic operations. The reactor does not add, subtract, multiply, divide, or execute iterative numerical steps. Instead, primality is decided through a physical propagation process.\r\n\r\nBy encoding the problem into a cyclic lattice and injecting a signal—optical, electrical, or quantum—the MCR transforms primality testing into a physical experiment. If the signal propagates and saturates the entire structure, the corresponding Mersenne number is prime; if destructive interference leaves persistent voids, it is composite.\r\n\r\nCrucially, the verdict is reached not by iterative computation, but by the completion of a single physical propagation event. 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