2011/02/28 by D. A. Goldston, Andrew Ledoan, A. H. Ledoan
Computer Science · Mathematics · #Analytic Number Theory Research #Champion #Coding theory and cryptography #Combinatorics #Computer science #Conjecture #Heuristics #Jumping #Law #Limits and Structures in Graph Theory #Mathematical economics #Mathematical optimization #Mathematics #Political science #Prime (order theory) #math.NT #msc:11N05 #msc:11N36 #msc:11P32
paper · pdf · doi:10.1112/s0025579315000078
published as Mathematika 61 (2015) 719-740 · 19 pages, 1 table
arxiv created 2012/06/28 · openalex publication_date 2015/05/04 · arxiv updated 2015/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 .