  A Prime Difference Champion (PDC) for primes up to $x$ is defined to be any
element of the set of one or more differences that occur most frequently among
all positive differences between primes $\le x$. Assuming an appropriate form
of the Hardy-Littlewood Prime Pair Conjecture we can prove that for
sufficiently large $x$ the PDCs run through the primorials. Numerical results
also provide evidence for this conjecture as well as other interesting
phenomena associated with prime differences. Unconditionally we prove that the
PDCs go to infinity and further have asymptotically the same number of prime
factors when counted logarithmically as the primorials.
