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- Title
The sequence of prime gaps is graphic.
- Authors
Erdős, Péter L.; Harcos, Gergely; Kharel, Shubha R.; Maga, Péter; Mezei, Tamás Róbert; Toroczkai, Zoltán
- Abstract
Let us call a simple graph on n ⩾ 2 vertices a prime gap graph if its vertex degrees are 1 and the first n - 1 prime gaps. We show that such a graph exists for every large n, and in fact for every n ⩾ 2 if we assume the Riemann hypothesis. Moreover, an infinite sequence of prime gap graphs can be generated by the so-called degree preserving growth process. This is the first time a naturally occurring infinite sequence of positive integers is identified as graphic. That is, we show the existence of an interesting, and so far unique, infinite combinatorial object.
- Subjects
RIEMANN hypothesis; INTEGERS
- Publication
Mathematische Annalen, 2024, Vol 388, Issue 2, p2195
- ISSN
0025-5831
- Publication type
Article
- DOI
10.1007/s00208-023-02574-1