  Combining the Hardy-Littlewood k-tuple conjecture with a heuristic
application of extreme-value statistics, we propose a family of estimator
formulas for predicting maximal gaps between prime k-tuples. Computations show
that the estimator a(log(x/a)-b) satisfactorily predicts the maximal gaps below
x, where a is the expected average gap between the same type of k-tuples,
a=O(log^k x). Heuristics suggest that maximal gaps between prime k-tuples near
x are approximately a*log(x/a), and thus have the order O(log^{k+1}x). The
distribution of maximal gaps around the trend curve a*log(x/a) is close to the
Gumbel distribution. We explore two implications of this model of gaps: record
gaps between primes and Legendre-type conjectures for prime k-tuples.
