The concept of prime number is so important that it has been generalized in different ways in various branches of mathematics. Generally, "prime" indicates minimality or indecomposability, in an appropriate sense. For example, the prime field is the smallest subfield of a field F containing both 0 and 1. It is either Q or the finite field with p elements, whence the name. Often a second, additional meaning is intended by using the word prime, namely that any object can be, essentially uniquely, decomposed into its prime components. For example, in knot theory, a prime knot is a knot which is indecomposable in the sense that it cannot be written as the knot sum of two nontrivial knots. Any knot can be uniquely expressed as a connected sum of prime knots. Prime models and prime 3-manifolds are other examples of this type.

The homophone for "knot" is "not."

The homophone for "not" is "knot."

A knot garden is formed by intricate shapes edged with box or some other slow growing easily shaped evergreens and the beds filled wth colourful low growing plants. Prime example is at Hampton Court in London.

Another name for the Hercules knot is the square knot.