---
tag: GJ6FJ4G5VC
kind: concept
name: Prime knot
msc: [57K10]
specializes: [QYEAZTYGPT]
sources:
  - url: https://en.wikipedia.org/wiki/Prime_knot
same_as:
  wikidata: Q1014491
  wikipedia: Prime knot
---

## Summary

A prime knot is a nontrivial [[knot|QYEAZTYGPT]] that is not the [[knot sum|AGZSZW7GYE]] of two nontrivial knots.
Schubert proved that every nontrivial knot is a knot sum of prime knots in a unique way, up to order.
So prime knots play the role for knots that prime numbers play for integers.
Knot tables list only prime knots.

## Explanations

### L1 human

Some knots are made by tying two simpler knots one after the other on the same string.
A prime knot is a knot that cannot be split like that.
The [[trefoil knot|VYTYSVHN4A]] is prime: it cannot be written as two smaller nontrivial knots.
The granny knot, which is two trefoils in a row, is not prime.
The plain unknotted loop is not counted as prime, just as $1$ is not a prime number.