The first few values are 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, ... (Sloane's A001223). Rankin has shown that

for infinitely many and for some constant (Guy 1994).

An integer is called a Jumping Champion if is the most frequently occurring difference between consecutive
primes for some (Odlyzko *et al. *).

**References**

Bombieri, E. and Davenport, H. ``Small Differences Between Prime Numbers.'' *Proc. Roy. Soc. A* **293**, 1-18, 1966.

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

Guy, R. K. ``Gaps between Primes. Twin Primes'' and ``Increasing and Decreasing Gaps.'' §A8 and A11 in
*Unsolved Problems in Number Theory, 2nd ed.* New York: Springer-Verlag, pp. 19-23 and 26-27, 1994.

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

Riesel, H. ``Difference Between Consecutive Primes.'' *Prime Numbers and Computer Methods for Factorization, 2nd ed.*
Boston, MA: Birkhäuser, p. 9, 1994.

Sloane, N. J. A. Sequence
A001223/M0296
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
*The Encyclopedia of Integer Sequences.* San Diego: Academic Press, 1995.

© 1996-9

1999-05-26