The k-tuple jumping champions among consecutive primes
Shaoji Feng, Xiaosheng Wu · Acta Arithmetica · 2012
The k-tuple jumping champions among consecutive primes by Shaoji Feng (Beijing) and Xiaosheng Wu (Hefei and Beijing) 1. Introduction.The search for the most probable difference among consecutive primes has been conducted for a long time.The problem was proposed by H. Nelson [N1, N2] in the 1977-78 volume of the Journal of Recreational Mathematics.Assuming the prime pair conjecture of G. H. Hardy and J. E. Littlewood [HL], P. Erdős and E. G. Straus [ES] showed in 1980 that there is no most likely difference, since they found that the most likely difference grows as the number considered becomes larger.J. H. Conway invented the term "jumping champion" to refer to the most common gap between consecutive primes not exceeding x.Let p n denote the nth prime.The jumping champions are the integers d for which the counting function N (x, d) = pn≤x pn-p n-1 =d 2010