This paper focuses on event prediction in an event sequence, particularly on distant event prediction. We aim at mining episode rules with a consequent temporally distant from the antecedent and with a minimal antecedent. To reach this goal, we propose an algorithm that determines the consequent of an episode rule at an early stage in the mining process, and that applies a span constraint on the antecedent and a gap constraint between the antecedent and the consequent. This algorithm has a complexity lower than that of state of the art algorithms, as it is independent of the gap between the antecedent and the consequent. In addition, the determination of the consequent at an early stage allows to filter out many non relevant rules early in the process, which results in an additional significant decrease of the running time. A new confidence measure is proposed, the temporal confidence, which evaluates the confidence of a rule in relation to the predefined gap. The temporal confidence is used to mine rules with a consequent that occurs mainly at a given distance. The algorithm is evaluated on an event sequence of social networks messages. We show that our algorithm mines minimal rules with a distant consequent, while requiring a small computation time. We also show that these rules can be used to accurately predict distant events.