Recurrence intervals between earthquakes strongly depend on history

We study the statistics of the recurrence times between earthquakes above a certain magnitude M$ in California. We find that the distribution of the recurrence times strongly depends on the previous recurrence time $\tau_0$. As a consequence, the conditional mean recurrence time $\hat \tau(\tau_0)$ between two events increases monotonically with $\tau_0$. For $\tau_0$ well below the average recurrence time $\ov{\tau}, \hat\tau(\tau_0)$ is smaller than $\ov{\tau}$, while for $\tau_0>\ov{\tau}$, $\hat\tau(\tau_0)$ is greater than $\ov{\tau}$. Also the mean residual time until the next earthquake does not depend only on the elapsed time, but also strongly on $\tau_0$. The larger $\tau_0$ is, the larger is the mean residual time. The above features should be taken into account in any earthquake prognosis.