2022/07/20 by Daniel Larsen · 1 citation
Mathematics · #Analytic Number Theory Research #History and Theory of Mathematics #Advanced Mathematical Identities
paper · doi:10.1093/imrn/rnac203
openalex publication_date 2022/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
Abstract Alford et al. [1] proved that there are infinitely many Carmichael numbers. In the same paper, they ask if a statement analogous to Bertrand’s postulate could be proven for Carmichael numbers. In this paper, we answer this question, proving the stronger statement that for all δ>0 and x sufficiently large in terms of δ , there exist at least e^\frac log x(log log x)2+δ Carmichael numbers between x and x+\frac x(log x)^\frac 12+δ .