{"id":"openai-math/Prime-Predecessors-with-an-Even-Number-of-Prime-Factors","pdf":"https://github.com/openai/math/blob/main/preprints/Prime-Predecessors-with-an-Even-Number-of-Prime-Factors-September-17-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Prime-Predecessors-with-an-Even-Number-of-Prime-Factors-September-17-2026","tags":["number-theory","primes","squarefree-integers","multiplicative-functions"],"score":0,"title":"Prime Predecessors with an Even Number of Prime Factors","domain":"Number theory","family":"011","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"We prove that there are infinitely many primes p for which $`p-1`$ is squarefree and has an even number of prime factors. Equivalently, there are infinitely many primes p with $`\\mu(p-1)=1`$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-17","reactions":{},"formalized":false,"family_title":"Prime-factor statistics of $`p-1`$"}