This page provides the lower bounds of the Gordian distance between all knots (possibly non-prime) with up to 10 crossings determined by the paper: Blanchfield pairing and Gordian distance (S. Friedl, T. Kitayama, and M. Suzuki).

• excel file
• table page

"K31" is 3_1, "K31m" is the mirror of 3_1, and "K31K41" is the connected sum of 3_1 and 4_1. Since prime factors of composite knots in the table are all reversible, the connected sum makes sense regardless of their orientations. The name of a knot follows KnotInfo. The values in the table are the lower bounds of the Gordian distance determined by the above paper. The lower bound "2" is given by applying Corollary 5.2 and "3" is by Proposition 5.4. In particular, 3 implies that other invariants (signature, Rasmussen s-invariant, Ozsvath-Szabo tau-invariant, rank of the first homology of the double branched cover, see Section 5.2) cannot detect this value. Moreover 3 implies that other invariants cannot detect this value and that the sum of unknotting numbers is also 3, namely the Gordian distance for this pair is 3. We cannot apply our results for the pair indicated by "0".