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This is the Prime Pages'
interface to our BibTeX database. Rather than being an exhaustive database,
it just lists the references we cite on these pages. Please let me know of any errors you notice.References: [ Home  Author index  Key index  Search ]
 ORW99
 A. Odlyzko, M. Rubinstein and M. Wolf, "Jumping champions," Experimental Math., 8:2 (1999) 107118. MR 2000f:11164
Abstract:
The asymptotic frequency with which pairs of primes below x differ by some fixed integer is understood heuristically, although not rigorously, through the HardyLittlewood ktuple conjecture. Less is known about the differences of consecutive primes. For all x between 1000 and 10^{12}, the most common difference between consecutive primes is 6. We present heuristic and empirical evidence that 6 continues as the most common difference (jumping champion) up to about x=1.7427· 10^{35}, where it is replaced by 30. In turn, 30 is eventually displaced by 210, which then is displaced by 2310, and so on. Our heuristic arguments are based on a quantitative form of the HardyLittlewood conjecture. The technical difficulties in dealing with consecutive primes are formidable enough that even that strong conjecture does not suffice to produce a rigorous proof about the behavior of jumping champions.
