Prime Difference Champions
Contribution to a Book
Springer Optimization and Its Applications
Andrei M. Raigorodskii, Michael Th. Rassias
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.
Differences between primes, Hardy–Littlewood prime pair conjecture, Jumping champion, Maximal prime gaps, Primorial numbers, Sieve methods, Singular series
Mathematics and Statistics
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