Prime Difference Function
 |
(1)
|
The first few values are 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, ... (OEIS A001223). Rankin has shown that
 |
(2)
|
for infinitely many 
and for some constant
(Guy 1994). At a March 2003 meeting on
elementary and analytic number in Oberwolfach, Germany, Goldston and Yildirim presented
an attempted proof that
 |
(3)
|
(Montgomery 2003). Unfortunately, this proof turned out to be flawed.
An integer 
is called a jumping
champion if 
is the most frequently
occurring difference between consecutive primes 
for some
(Odlyzko et al.).
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