Prime Gap Structure
The article describes a repository presenting three major results related to prime gap structure. It introduces the Leftmost Minimum-Divisor Rule, a frozen hierarchical finite-state model for prime-gap types, and a deterministic prime generator that infers successor primes without traditional primality tests. These results aim to model and generate primes using structural properties within prime gaps.
- ▪The Leftmost Minimum-Divisor Rule selects the leftmost interior composite with the smallest divisor count in a prime gap.
- ▪The Prime Gap Generative Model v1.0 exhibits a stable 14-state core on the reduced gap-type surface with a Semiprime Wheel Attractor as its dominant dynamical object.
- ▪The PGS Prime Generator infers the successor prime q from deterministic chamber state without trial division, sieves, or probabilistic tests.
- ▪The generator outputs minimal records of the form {"p": ..., "q": ...}, excluding diagnostics from the output stream.
- ▪The current production version of the PGS Prime Generator is v1.1.
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Prime Gap Structure This repository now carries three major prime-gap results: a proved local arithmetic selection law inside prime gaps, with the live proof reference in PROOF.md; a frozen hierarchical finite-state model for reduced prime-gap types. a PGS Prime Generator that infers the successor prime from deterministic prime-gap-structure chamber state, without trial division, Miller-Rabin, sieve generation, fallback prime search, or nextprime inside generation. Take the consecutive primes 23 and 29. The integers between them are 24, 25, 26, 27, 28. Their divisor counts are: d(24) = 8 d(25) = 3 d(26) = 4 d(27) = 4 d(28) = 6 So 25 wins this gap because it has the smallest divisor count present. Now take 89 and 97. The interior integers are 90, 91, 92, 93, 94, 95, 96.
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Excerpt limited to ~120 words for fair-use compliance. The full article is at GitHub.