Computational modeling demonstrates emergent linear geometry and interval alternation across prime gaps up to one trillion, suggesting hidden deterministic order in prime distributions.
The paper investigates the spatial geometry of prime number distribution on a plane. Based on the author's algorithm of cyclic 90-degree vector construction utilizing intervals between consecutive prime numbers, a series of large-scale computational experiments was conducted on a sample of up to 1 trillion numbers. During the computer simulation, protected from the errors of Carmichael numbers, a ultra-detailed "comma-shaped" pattern was captured at small scales, which stabilizes into a strict straight line when moving to large and ultra-large prime numbers. The results obtained experimentally prove the internal interdependence of prime numbers and reveal a previously unknown law of alternation between long and short intervals. Keywords: prime numbers, prime gaps, fractals, law of alternation, visualization algorithms, Carmichael numbers, experimental mathematics. Аннотация: В работе исследуется пространственная геометрия распределения простых чисел на п
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viacheslav orekhov (2026) studied this question.
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