The growth of the number of prime knots

Abstract

A fundamental and interesting question in knot theory is: Question 1. How many prime knots of n crossings are there ? Over time, knot theorists have answered this question for n ≤ 13 by the method of exhaustion: one writes down a list of all possible knots of n crossings, and then works hard to eliminate duplications from the list [12]. A perhaps easier question is the following: