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@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 }
}