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In
knot theory In the mathematical field of topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot ...
,
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 ...
s are those knots that are
indecomposable Indecomposability or indecomposable may refer to any of several subjects in mathematics: * Indecomposable module, in algebra * Indecomposable distribution, in probability * Indecomposable continuum, in topology * Indecomposability (intuitionist ...
under the operation of
knot sum In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds. Its effect is to join two given manifolds together near a chosen point on each. This construction plays a key role in the classific ...
. The prime knots with ten or fewer crossings are listed here for quick comparison of their properties and varied naming schemes.


Table of prime knots


Six or fewer crossings


Seven crossings


Eight crossings


Nine crossings


Ten crossings


Higher

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Conway knot In mathematics, in particular in knot theory, the Conway knot (or Conway's knot) is a particular knot with 11 crossings, named after John Horton Conway. It is related by mutation to the Kinoshita–Terasaka knot, with which it shares the sam ...
11n34 *
Kinoshita–Terasaka knot In knot theory, the Kinoshita–Terasaka knot is a particular prime knot. It has 11 crossings. The Kinoshita–Terasaka knot has a variety of interesting mathematical properties. It is related by mutation to the Conway knot, with which it shares ...
11n42


Table of prime links


Seven or fewer crossings


Higher


See also

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List of knots This list of knots includes many alternative names for common knots and lashings. Knot names have evolved over time, and there are many conflicting or confusing naming issues. The overhand knot, for example, is also known as the thumb knot. The ...
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List of mathematical knots and links This article contains a list of mathematical knots and links. See also list of knots, list of geometric topology topics. Knots Prime knots *01 knot/Unknot - a simple un-knotted closed loop *31 knot/Trefoil knot - (2,3)-torus knot, the two lo ...
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Knot tabulation Ever since Sir William Thomson's vortex theory, mathematicians have tried to classify and tabulate all possible knots. As of May 2008, all prime knots up to 16 crossings have been tabulated. The major challenge of the process is that many app ...
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(−2,3,7) pretzel knot In geometric topology, a branch of mathematics, the (−2, 3, 7) pretzel knot, sometimes called the Fintushel–Stern knot (after Ron Fintushel and Ronald J. Stern), is an important example of a pretzel knot which exhibits various ...


Notes


External links

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KnotInfo
, ''Indiana.edu''. {{DEFAULTSORT:Prime knots Knot theory Mathematics-related lists