  We adopt a physically motivated empirical approach to the characterisation of
the distributions of twin and triplet primes within the set of primes, rather
than in the set of all natural numbers. Remarkably, the occurrences of twins or
triplets in any finite sequence of primes are like fixed-probability random
events. The respective probabilities are not constant, but instead depend on
the length of the sequence in ways that we have been able to parameterise. For
twins the ``decay constant'' decreases as the reciprocal of the logarithm of
the length of the sequence, whereas for triplets the falloff is faster:
decreasing as the square of the reciprocal of the logarithm of the number of
primes. The manner of the decrease is consistent with the Hardy--Littlewood
Conjectures, developed using purely number theoretic tools of analysis.
