## Jumping Champion

An integer is called a Jumping Champion if is the most frequently occurring difference between consecutive primes for some (Odlyzko et al. ). This term was coined by J. H. Conway in 1993. There are occasionally several jumping champions in a range. Odlyzko et al. give a table of jumping champions for , consisting mainly of 2, 4, and 6. 6 is the jumping champion up to about , at which point 30 dominates. At , 210 becomes champion, and subsequent Primorials are conjectured to take over at larger and larger . Erdös and Straus (1980) proved that the jumping champions tend to infinity under the assumption of a quantitative form of the -tuples conjecture.

References

Erdös, P.; and Straus, E. G. Remarks on the Differences Between Consecutive Primes.'' Elem. Math. 35, 115-118, 1980.

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, 1994.

Nelson, H. Problem 654.'' J. Recr. Math. 11, 231, 1978-1979.

Odlyzko, A.; Rubinstein, M.; and Wolf, M. Jumping Champions.'' http://www.research.att.com/~amo/doc/recent.html.