Composite run around primes
Abstract
We prove that for every positive even integer $2n$, there exist infinitely many sequences of $2n-1$ consecutive composite integers, with each sequence immediately followed or preceded by a prime. Our approach uses factorial and primorial constructions combined with Dirichlet's theorem on arithmetic progressions, yielding explicit formulas that determine the positions of these sequences. This result offers new insights into the distribution of primes relative to consecutive composite numbers.
Fields of Study & Subjects
Analytic Number Theory Research
Limits and Structures in Graph Theory
Mathematics and Applications
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 29 June 2026
- Language
- EN
- Document type
- Preprint