Two-dimensional sequential data organization is considered, where each dimension corresponds to one of two attributes. A query on the data is a figure on the storage. The elementary figure is a rectangle, and any figure can be described by a set of rectangles. Prime rectangles are defined as the ones relevant to any figure description, and the problem of finding a minimal description is studied. In particular, the upper bound to the number of prime rectangles is derived, and a cubic algorithm to find all such rectangles is given. Descriptions composed of all disjoint rectangles are the subject of the second part or this paper.