Prime Difference Champions

S. Funkhouser (), D. A. Goldston (), D. Sengupta () and J. Sengupta ()
Additional contact information
S. Funkhouser: Trident Technical College
D. A. Goldston: San José State University
D. Sengupta: Elizabeth City State University
J. Sengupta: Elizabeth City State University

A chapter in Discrete Mathematics and Applications, 2020, pp 207-236 from Springer

Abstract: Abstract A Prime Difference Champion (PDC) for primes up to x is defined to be any element of the set of one or more differences that occur most frequently among all positive differences between primes ≤ x. Assuming an appropriate form of the Hardy–Littlewood Prime Pair Conjecture we can prove that for sufficiently large x the PDCs run through the primorials. Numerical results also provide evidence for this conjecture as well as other interesting phenomena associated with prime differences. Unconditionally we prove that the PDCs go to infinity and further have asymptotically the same number of prime factors when counted logarithmically as the primorials.

Keywords: Differences between primes; Hardy–Littlewood prime pair conjecture; Jumping champion; Maximal prime gaps; Primorial numbers; Sieve methods; Singular series; Primary 11N05; Secondary 11P32, 11N36 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/978-3-030-55857-4_9

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