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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 ]

Item(s) in original BibTeX format

@article{ORW99,
	author={A. Odlyzko and M. Rubinstein and M. Wolf},
	title={Jumping Champions},
	abstract={The asymptotic frequency with which pairs of primes below $x$ differ by
		some fixed integer is understood heuristically, although not rigorously,
		through the Hardy-Littlewood k-tuple 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 $x=1.7427\cdot 10^{35}$, 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 Hardy-Littlewood 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.},
	journal= expm,
	volume= 8,
	year= 1999,
	pages={107-118},
	number= 2 ,
	mrnumber={2000f:11164 }
}

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