Prime Difference Champions
Publication Date
1-1-2020
Document Type
Contribution to a Book
Publication Title
Springer Optimization and Its Applications
Editor
Andrei M. Raigorodskii, Michael Th. Rassias
Volume
165
DOI
10.1007/978-3-030-55857-4_9
First Page
207
Last Page
236
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
Department
Mathematics and Statistics
Recommended Citation
S. Funkhouser, D. A. Goldston, D. Sengupta, and J. Sengupta. "Prime Difference Champions" Springer Optimization and Its Applications (2020): 207-236. https://doi.org/10.1007/978-3-030-55857-4_9
