A jumping champion is a positive integer that is the most frequently occurring difference between consecutive primes 
for some 
(Odlyzko et al. 1999). For a fixed 
, denote such a difference by 
. The term was coined by J. H. Conway in
1993 (Odlyzko et al. 1999, p. 109). There are occasionally several jumping
champions in a range. The scatter plots above
show the jumping champions for small 
, and the ranges of numbers having
given jumping champion sets are summarized in the following table.
 |  |
| 1 | 3 |
| 1, 2 | 5 |
| 2 | 7-100, 103-106, 109-112, ... |
| 2, 4 | 101-102, 107-108, 113-130, ... |
| 4 | 131-138, ... |
| 2, 4, 6 | 179-180, 467-490, ... |
| 2, 6 | 379-388, 421-432, ... |
| 6 | 389-420, ... |
Odlyzko et al. (1999) give a table of jumping champions for 
, consisting mainly of 2, 4, and 6. Their heuristic
estimates predict that 6 remains the jumping champion up to about 
, when 30 takes over, and that
210 becomes champion at about 
. The conjectured
jumping champions greater than 1 are 2, 4, 6, 30, 210, 2310, 30030, ... (OEIS A121069), consisting of 4 together with the primorials greater than 1 (Odlyzko et al. 1999,
p. 108). Erdős and Straus (1980) proved that the jumping champions tend
to infinity under the assumption of a quantitative form
of the k-tuple conjecture.
Wolf gives a table of approximate values 
at which the primorial 
will become a champion. An estimate
for 
is given by
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