Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 029-01. Primitive roots for every admissible integer base
Manuscript map · lines 2985–2994
OpenAI@2026-10-07#rem:oai-p-029-01
Authors: OpenAI. Family 029.
Title: Primitive roots for every admissible integer base.
Abstract: We prove the infinitude assertion in Artin's primitive root conjecture: for every integer a that is neither −1 nor a square, there are at least $c_a x/({}log x){}2$ primes in $(x,2x)$ with primitive root a, for some $c_a{}gt 0$ and every sufficiently large x.
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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