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.