THE JUMPING CHAMPION CONJECTURE
2015; Wiley; Volume: 61; Issue: 3 Linguagem: Inglês
10.1112/s0025579315000078
ISSN2041-7942
AutoresD. A. Goldston, Andrew Ledoan,
Tópico(s)Coding theory and cryptography
ResumoAn 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 .
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