The Size of the Fundamental Solutions of Consecutive Pell Equations

] (D) = log X1/ log X0. We prove here that ] (D) can be arbitrarily large. Indeed, we exhibit an infinite family of values of D for which ] (D) ^ D1/6/ log D. We also provide some heuristic reasoning which suggests that there exists an infinitude of values of D for which ] (D) ^`_ D log log D/ log D, and that this is the best possible result under the Extended Riemann Hypothesis. Finally, we present some numerical evidence in support of this heuristic.