  Flat plumbing basket surfaces of links were introduced to study the geometry
of the complement of the links. These flat plumbing basket surface can be
presented by a sequential presentation known as flat plumbing basket code first
found by Furihata, Hirasawa and Kobayashi. The minimum number of flat plumbings
to obtain a flat plumbing basket surfaces of a link is defined to be the flat
plumbing basket number of the given link. In present article, we use these
sequential presentations to find the complete classification theorem of prime
knots whose flat plumbing basket number $6$ or less. As applications, this
result improves the work of Hirose and Nakashima which finds the flat plumbing
basket number of prime knots up to 9 crossings.
