To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Languages
Recent
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds

# Prime knot

In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable. Specifically, it is a non-trivial knot which cannot be written as the knot sum of two non-trivial knots. Knots that are not prime are said to be composite knots or composite links. It can be a nontrivial problem to determine whether a given knot is prime or not.

A family of examples of prime knots are the torus knots. These are formed by wrapping a circle around a torus p times in one direction and q times in the other, where p and q are coprime integers.

The simplest prime knot is the trefoil with three crossings. The trefoil is actually a (2, 3)-torus knot. The figure-eight knot, with four crossings, is the simplest non-torus knot. For any positive integer n, there are a finite number of prime knots with n crossings. The first few values (sequence A002863 in the OEIS) are given in the following table.

 n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Number of prime knots with n crossings 0 0 1 1 2 3 7 21 49 165 552 2176 9988 46972 253293 1388705 Composite knots 0 0 0 0 0 2 1 4 ... ... ... ... Total 0 0 1 1 2 5 8 25 ... ... ... ...

Enantiomorphs are counted only once in this table and the following chart (i.e. a knot and its mirror image are considered equivalent).

A chart of all prime knots with seven or fewer crossings, not including mirror-images. (The unknot is not considered prime.)

## Schubert's theorem

A theorem due to Horst Schubert states that every knot can be uniquely expressed as a connected sum of prime knots.[1]