Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 029-02. Simultaneous primitive roots: a conditional lower bound for prime bases
Manuscript map · lines 2995–3004
OpenAI@2026-10-07#rem:oai-p-029-02
Authors: OpenAI. Family 029.
Title: Simultaneous primitive roots: a conditional lower bound for prime bases.
Abstract: For every fixed finite set of distinct positive primes, we prove that at least $cx/({}log x){}2$ primes in $(x,2x)$ have every member of the set as a primitive root, for some c > 0 and all sufficiently large x. The result assumes four explicitly stated analytic and sieve inputs from the companion paper on primitive roots for admissible integer bases.
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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