Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 011-02. The Poisson-Dirichlet law for prime predecessors
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OpenAI@2026-10-07#rem:oai-p-011-02
Authors: OpenAI. Family 011.
Title: The Poisson-Dirichlet law for prime predecessors.
Abstract: For a prime p chosen uniformly from $3{}le p{}le x$, list the prime factors of $p-1$ in decreasing order, with multiplicity. As $x{}to{}infty$, their logarithms, divided by ${}log(p-1)$, converge in every finite joint distribution to the Poisson–Dirichlet distribution with parameter one. This proves the conjecture of Ford, Konyagin and Luca.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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