{"id":"openai-math/The-Poisson-Dirichlet-Law-for-Prime-Predecessors","pdf":"https://github.com/openai/math/blob/main/preprints/The-Poisson-Dirichlet-Law-for-Prime-Predecessors-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Poisson-Dirichlet-Law-for-Prime-Predecessors-September-24-2026","tags":["number-theory","probabilistic-number-theory","prime-factorization"],"score":0,"title":"The Poisson-Dirichlet law for prime predecessors","domain":"Number theory","family":"011","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Prime-factor statistics of $`p-1`$"}