OpenAI research collection · 2 manuscripts · Source checked 2026-10-19
Proves the infinitude assertion in Artin's primitive root conjecture for every integer a that is neither −1 nor a square. For each such base, at least c_a x/(log x)^2 primes in every sufficiently large interval (x,2x) have primitive root a, with c_a> 0.
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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> 0 and every sufficiently large x.
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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…
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 exact PDF is not listed in the imported formalization catalogue. Family scope notes may contain further information.
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