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

• prime number

• prime geodesic

References

• Adams, Colin, C., 1994, The Knot Book—An elementary Introduction to the Mathematical Theory of Knots, W. H. Freedman and Co.