Year: 2015
Type: article
Abstract: An integer is called a jumping champion for a given if is the most common gap between consecutive primes up to . Occasionally, several gaps are equally common. Hence, there can be more than one jumping champion for the same . In 1999, Odlyzko et al provided convincing heuristics and empirical evidence for the truth of the hypothesis that the jumping champions greater than 1 are 4 and the primorials . In this paper, we prove that an appropriate form of the Hardy–Littlewood prime -tuple conjecture for prime pairs and prime triples implies that all sufficiently large jumping champions are primorials and that all sufficiently large primorials are jumping champions over a long range of .
Source: Mathematika
Authors: Daniel A. Goldston, Andrew H. Ledoan
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1546733152