Prime Difference Function
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. SequenceA001223/M0296in ``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.
- Sturm-Liouville Equation
- Sturm-Liouville Theory
- Sturm Theorem
- Stäckel Determinant
- Stérmer Number
- Stöhr Sequence
- Subalgebra
- Subanalytic
- Subfactorial
- Subfield
- Subgraph
- Subgroup
- Sublime Number
- Submanifold
- Submatrix
- Subnormal
- Subordinate Norm
- Subscript
- Subsequence
- Subset
- Subspace
- Substitution Group
- Substitution Map
- Subtend
- Subtraction