Prime knot

It can be a nontrivial problem to determine whether a given knot is prime or not.

The simplest prime knot is the trefoil with three crossings.

For any positive integer n, there are a finite number of prime knots with n crossings.

The first few values for exclusively prime knots (sequence A002863 in the OEIS) and for prime or composite knots (sequence A086825 in the OEIS) are given in the following table.

Enantiomorphs are counted only once in this table and the following chart (i.e. a knot and its mirror image are considered equivalent).

Simplest prime link
A chart of all prime knots with seven or fewer crossings , not including mirror-images, plus the unknot (which is not considered prime).