nLab prime knot

Idea

A prime knot is a knot that cannot be decomposed, that is to say, a knot that cannot be constructed from the knot sum of two non-trivial knots.

In the context of knot complexity?, whether or not a knot is prime is nontrivial. Any knot which is not prime is called a composite knot.

Examples

• The unknot

• The fundamental example of a prime knot is the trefoil with three crossings?

• The family of torus knots

Related concepts

• composite knot

• prime number

• prime geodesic

References

Most monographs on knot theory speak about prime knots, e.g.

• Colin C. Adams, The Knot Book – An elementary Introduction to the Mathematical Theory of Knots, W. H. Freedman and Co. (1994) [ISBN:978-0-8218-3678-1]

Lecture notes:

• Marcos Morinigo, Prime factorization of knots [pdf]