Large and Small Knots
A knot is called large if there is a closed incompressible surface (pi_1 injective) in its complement. Otherwise it is called small. The data used in KnotInfo is based on the work of Benjamin Burton, Alexander Coward, and Stephan Tillmann, with data available at a website maintained by Benjamin.
B. Burton, "Benjamin Burton - Code," www.maths.uq.edu.au/~bab/code/ .
B. Burton, A. Coward, and S. Tillmann, "Computing closed essential surfaces in knot complements," Math ArXiv, http://arxiv.org/abs/1212.1531 .