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Abstract / Synopsis

Prime numbers have resisted systematic description for over two millennia. We propose that part of the difficulty may lie in an insufficiently attentive examination of one’s own hands. In particular, we assign the natural numbers to the joints of the human hand according to a cyclic traversal protocol, and make a handful of observations which can naturally be translated into number-theoretic properties of prime numbers. We show that these properties lead us to natural activation thresholds of a unified three-phase sieve algorithm — the resulting framework provides, for the first time, a zone-based partition of the admissible space with explicit boundaries at p and #p, free of inclusion-exclusion complexity. We discuss how this architecture adapts naturally to pair-based sieves, offering a clean structural foundation from which the Twin Prime Conjecture and Goldbach’s Conjecture may be approached without the analytic overhead that has historically made them intractable.

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