{"id":"openai-math/Primitive-roots-for-every-admissible-integer-base","pdf":"https://github.com/openai/math/blob/main/preprints/Primitive-roots-for-every-admissible-integer-base-October-4-2026/primitive-roots-all-integer-bases.pdf","url":"https://github.com/openai/math/tree/main/preprints/Primitive-roots-for-every-admissible-integer-base-October-4-2026","tags":["number-theory","primitive-roots","artin-conjecture","prime-distribution"],"score":0,"title":"Primitive roots for every admissible integer base","domain":"Number theory","family":"029","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"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 .","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-10-04","reactions":{},"discussion":[{"url":"https://galoisrepresentations.org/2026/10/08/a-brief-digest-of-some-new-openai-results/#:~:text=So%20again%2C%20this%20is%20an%20interesting%20type%20of%20argument%20which%20I%20don%E2%80%99t%20find%20particularly%20surprising.","kind":"web","site":"galoisrepresentations.org","text":"So again, this is an interesting type of argument which I don’t find particularly surprising. But no one was going to write this paper, which depends on the quasi-Riemann hypothesis for Dirichlet \\(L\\)-functions, without knowing anything about general Dedekind \\(L\\)-functions. And this brings us…","added":"2026-10-24","title":"A Brief Digest of Some New OpenAI Results | Persiflage","author":"Persiflage"}],"formalized":false,"family_title":"Primitive roots for every admissible integer base"}