1. A character input prediction apparatus comprising: a first operation input unit configured to obtain information of a first character input operation that is performed by a user using a character key layout display in which a plurality of character keys are arranged; a dictionary storage unit configured to store a dictionary including a plurality of candidate character strings; a character key layout management unit configured to store a character key layout showing the arrangement of the plurality of character keys in the character key layout display; a first indication movement detection unit configured to detect a first indication position and a first indication direction in the character key layout display from the information of the first character input operation, the first indication position showing a position of the first character input operation, and the first indication direction showing a movement direction of the first character input operation; a first filter generation unit configured to determine a first character range in the character key layout display using the first indication position, the first indication direction, and the character key layout, the first character range being located in the first indication direction with the first indication position as a base point; and a dictionary search unit configured to search the plurality of candidate character strings included in the dictionary, for a predictive character string that includes any character included in the first character range.