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Non-trivial knot which cannot be written as the knot sum of two non-trivial knots
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
Prime_knot
In knot theory, prime knots are those knots that are indecomposable under the operation of knot sum. The prime knots with ten or fewer crossings are listed
List_of_prime_knots
Unique knot with a crossing number of four
unknot and the trefoil knot. The figure-eight knot is a prime knot. The name is given because tying a normal figure-eight knot in a rope and then joining
Figure-eight knot (mathematics)
Figure-eight_knot_(mathematics)
Simplest non-trivial closed knot with three crossings
In knot theory, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot. The trefoil can be obtained by joining the two
Trefoil_knot
Study of mathematical knots
In 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,
Knot_theory
Prime knot named for John Horton Conway
In mathematics, specifically in knot theory, the Conway knot (or Conway's knot) is a particular knot with 11 crossings, named after John Horton Conway
Conway_knot
Specific knot in knot theory with 11 crossings
In knot theory, the Kinoshita–Terasaka knot is a particular prime knot with 11 crossings. It is named after Japanese mathematicians Shinichi Kinoshita
Kinoshita–Terasaka_knot
twist knot with four twists 62 knot - a prime knot with crossing number six 63 knot - a prime knot with crossing number six 71 knot, septafoil knot, (7
List of mathematical knots and links
List_of_mathematical_knots_and_links
Mathematical knot with crossing number 7
In knot theory, the Pentatwist knot, also known as the five-twist knot, or the 72, is one of seven prime knots with crossing number seven. It is the fifth
7_2_knot
Mathematical knot with crossing number 7
In knot theory, the 71 knot, also known as the septoil knot, the septafoil knot, or the (7, 2)-torus knot, is one of seven prime knots with crossing number
71_knot
Mathematical knot with crossing number 5
In knot theory, the cinquefoil knot, also known as Solomon's seal knot or the pentafoil knot, is one of two knots with crossing number five, the other
Cinquefoil_knot
Mathematical knot with crossing number 5
ϕ ≤ 2 π {\displaystyle 0\leq \phi \leq 2\pi } . The three-twist knot is a prime knot, and it is invertible but not amphichiral. Its Alexander polynomial
Three-twist_knot
Mathematical knot with crossing number 7
In mathematical knot theory, 74 is the name of a 7-crossing knot which can be visually depicted in a highly-symmetric form, and so appears in the symbolism
74_knot
Topics referred to by the same term
3-manifolds Prime element, in algebra Prime form of a Riemann surface Prime ideal, a subset of a ring Prime knot, a knot that cannot be written as the knot sum
Prime_(disambiguation)
Minimum number of times a specific knot must be passed through itself to become untied
unknotting number at least two, and therefore every knot with unknotting number one is a prime knot. The unknotting number is not additive under connected
Unknotting_number
Integer-valued knot invariant; least number of crossings in a knot diagram
mathematical area of knot theory, the crossing number of a knot is the smallest number of crossings of any diagram of the knot. It is a knot invariant. By way
Crossing_number_(knot_theory)
Embedding of the circle in three dimensional Euclidean space
mathematics, a knot is an embedding of the circle (S1) into three-dimensional Euclidean space, R3 (also known as E3). Often two knots are considered equivalent
Knot_(mathematics)
Knot which lies on the surface of a torus in 3-dimensional space
In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies
Torus_knot
Attempt to classify and tabulate all possible knots
tabulate all possible knots. By 1998, all 1.7 million prime knots up to 16 crossings had been tabulated, and by 2020 all 350 million knots up to 19 crossings
Knot_tabulation
Number divisible only by 1 and itself
essentially uniquely, decomposed into its prime components. For example, in knot theory, a prime knot is a knot that is indecomposable in the sense that
Prime_number
Stevedore knot (mathematics), a prime knot with crossing number 6 Three-twist knot is the twist knot with three-half twists, also known as the 52 knot. Trefoil
List_of_knot_theory_topics
Mathematical knot with crossing number 6
In knot theory, the stevedore knot is one of three prime knots with crossing number six, the others being the 62 knot and the 63 knot. The stevedore knot
Stevedore_knot_(mathematics)
Loop seen as a trivial knot
of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the unknot is a closed loop of rope without a knot tied
Unknot
Type of mathematical knot
mathematical theory of knots, a satellite knot is a knot that contains an incompressible, non boundary-parallel torus in its complement. Every knot is either hyperbolic
Satellite_knot
Mathematical knot with crossing number 6
In knot theory, the 62 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 63 knot. This knot is sometimes
62_knot
enabled early knot tabulators, such as Tait, to construct tables with relatively few mistakes or omissions. The simplest non-alternating prime knots have 8 crossings
Alternating_knot
Mathematical knot with crossing number 6
In knot theory, the 63 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 62 knot. It is alternating
63_knot
Two interlinked loops with five structural crossings
In knot theory, the Whitehead link, named for J. H. C. Whitehead, is one of the most basic links. It can be drawn as an alternating link with five crossings
Whitehead_link
Knot that is not equivalent to its mirror image
for prime, alternating knots. Both possible trefoil knots. The left-handed trefoil knot. The right-handed trefoil knot. The simplest chiral knot is the
Chiral_knot
Branch of mathematics
Zbl 0208.48701. Adams, Colin (2004). The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. American Mathematical Society. ISBN 978-0-8218-3678-1
Topology
Simplest nontrivial knot link
In mathematical knot theory, the Hopf link is the simplest nontrivial link with more than one component. It consists of two circles linked together exactly
Hopf_link
Prime knot with crossing number 10
theory of knots, the Perko pair, named after Kenneth Perko, is a pair of entries in classical knot tables that actually represent the same knot. In Dale
Perko_pair
Mathematical invariant of a knot or link
of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Specifically, it is an invariant of an oriented knot or
Jones_polynomial
Three linked but pairwise separated rings
Thistlethwaite in a list of all prime links with up to 13 crossings. In the tables of knots and links in Dale Rolfsen's 1976 book Knots and Links, extending earlier
Borromean_rings
Knot that bounds an embedded disk in 4-space
A slice knot is a mathematical knot in 3-dimensional space that bounds an embedded disk in 4-dimensional space. A knot K ⊂ S 3 {\displaystyle K\subset
Slice_knot
Function of a knot that takes the same value for equivalent knots
mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots. The equivalence
Knot_invariant
Knot invariant
a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II discovered this, the first knot polynomial
Alexander_polynomial
Way to join two given mathematical manifolds together
by a prime knot. Proof of commutativity can be seen by letting one summand shrink until it is very small and then pulling it along the other knot. The
Connected_sum
Motif with two doubly-interlinked loops
classified as a link, and is not a true knot according to the definitions of mathematical knot theory. The Solomon's knot consists of two closed loops, which
Solomon's_knot
Connected sum of two trefoil knots with opposite chirality
In knot theory, the square knot is a composite knot obtained by taking the connected sum of a trefoil knot with its reflection. It is closely related
Square_knot_(mathematics)
Type of knot in knot theory
Bridge number 2 In the mathematical field of knot theory, a 2-bridge knot is a knot which can be regular isotoped so that the natural height function given
2-bridge_knot
Knots Landing is an American prime time television soap opera that originally aired on CBS from December 27, 1979, to May 13, 1993. A spin-off of Dallas
List of Knots Landing episodes
List_of_Knots_Landing_episodes
again only true for alternating knots: non-alternating amphichiral knot with crossing number 15 exist. Prime knot Tangle (knot theory) Lickorish, W. B. Raymond
Tait_conjectures
Knot defined by parametric equations defining Lissajous curves
In knot theory, a Lissajous knot is a knot defined by parametric equations of the form x = cos ( n x t + ϕ x ) , y = cos ( n y t + ϕ y ) , z = cos
Lissajous_knot
Connected sum of two trefoil knots with same chirality
In knot theory, the granny knot is a composite knot obtained by taking the connected sum of two identical trefoil knots. It is closely related to the square
Granny_knot_(mathematics)
Family of mathematical knots
In knot theory, a branch of mathematics, a twist knot is a knot obtained by repeatedly twisting a closed loop and then linking the ends together. (That
Twist_knot
Flat woven decorative knot
The carrick mat is a flat woven decorative knot which can be used as a mat or pad. Its name is based on the mat's decorative-type carrick bend with the
Carrick_mat
Class of ornamental knots
A Turk's head knot, sometimes known as a sailor's knot, is a decorative knot with a variable number of interwoven strands forming a closed loop. The name
Turk's_head_knot
Type of mathematical link
three-twist knot) 61 knot (the stevedore knot) 62 knot 63 knot 74 knot 10 161 knot (the "Perko pair" knot) 12n242 knot SnapPea Hyperbolic volume (knot) Colin
Hyperbolic_link
Natural number
deficient number. a sphenic number. a tetrahedral number. the number of prime knots with 10 crossings. the sum of the sums of the divisors of the first 14
165_(number)
Type of mathematical knot
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
(−2,3,7)_pretzel_knot
Graph topology applied to electrical and communications circuits, or biomolecules
connected sum of prime knots, which are themselves undecomposable. Circuit topology splits any entangled chains (including prime knots) into basic structural
Circuit_topology
президента Южной Осетии". Caucasian Knot. Retrieved 11 September 2026. "Габараев Эдуард Иналович". Caucasian Knot. Retrieved 17 September 2026. "Инициативная
2026 South Ossetian presidential election
2026_South_Ossetian_presidential_election
Natural number
prime number 1,336,336 = 11562 = 344 1,346,269 = Fibonacci number, Markov number 1,367,631 = 1113, palindromic cube 1,388,705 = number of prime knots
1,000,000
Mathematical notation for describing the structure of knots
In the mathematical field of knot theory, the Dowker–Thistlethwaite (DT) notation or code, for a knot diagram is a sequence of even integers. The notation
Dowker–Thistlethwaite notation
Dowker–Thistlethwaite_notation
Knot that can't be tied in a string of constant diameter
In the mathematical theory of knots, a knot is tame if it can be "thickened", that is, if there exists an extension to an embedding of the solid torus
Wild_knot
Types of knots (and links) Torus knot Prime knot Alternating knot Hyperbolic link Knot invariants Crossing number Linking number Skein relation Knot polynomials
List of geometric topology topics
List_of_geometric_topology_topics
Operations are used to investigate whether knots are equivalent, prime or reduced. Knot moves or operations include the flype, Habiro move, Markov moves
Knot_operation
terms; semiperfect. A002858 Prime knots 0, 0, 1, 1, 2, 3, 7, 21, 49, 165, 552, 2176, 9988, ... The number of prime knots with n crossings. A002863 Carmichael
List_of_integer_sequences
Difference in shape from a mirror image
chiral. For example, the unknot and the figure-eight knot are achiral, whereas the trefoil knot is chiral. In physics, chirality may be found in the spin
Chirality
Deputy head of government of the de facto independent republic
announced his resignation as prime minister on 26 July 2016, accepted on the same day by Khajimba. In an interview with Caucasian Knot, Mikvabia stated that
Prime_Minister_of_Abkhazia
Property in knot theory
In the mathematical field of knot theory, the tricolorability of a knot is the ability of a knot to be colored with three colors subject to certain rules
Tricolorability
known as knot theory, there is an analogue of the fundamental theorem of arithmetic: the decomposition of a knot into a sum of prime knots is essentially
Essentially_unique
American actress
actress, best-known for her role as Olivia Cunningham in the CBS prime time soap opera, Knots Landing. Crowe was born in Los Angeles, California, a daughter
Tonya_Crowe
Natural number
fifth powers: 125 = 45 + 55 + 65 + 75 + 95 + 115 253,293 = number of prime knots with 15 crossings 255,168 = number of ways to play tic tac toe 262,144
100,000
Type of mathematical knot
In the mathematical area of knot theory, a ribbon knot is a knot that bounds a self-intersecting disk with only ribbon singularities. Intuitively, this
Ribbon_knot
Actor
roles on television. He played Gary Ewing in the CBS prime time soap operas Dallas and its spin-off Knots Landing (1979–1993), and had a recurring role portraying
Ted_Shackelford
Area of mathematics
there is an analogy between knots and prime numbers in which one considers "links" between primes. The triple of primes (13, 61, 937) are "linked" modulo
Arithmetic_topology
Complement of a knot in three-sphere
In mathematics, the knot complement of a tame knot K is the space where the knot is not. If a knot is embedded in the 3-sphere, then the complement is
Knot_complement
Polynomials arising in knot theory
field of knot theory, the HOMFLY polynomial or HOMFLYPT polynomial, sometimes called the generalized Jones polynomial, is a 2-variable knot polynomial
HOMFLY_polynomial
Fundamental group of a knot complement
a knot is an embedding of a circle into 3-dimensional Euclidean space. The knot group of a knot K is defined as the fundamental group of the knot complement
Knot_group
Mathematical knot
In knot theory, a branch of mathematics, a knot or link K {\displaystyle K} in the 3-dimensional sphere S 3 {\displaystyle S^{3}} is called fibered or
Fibered_knot
Group whose operation is a composition of braids
§ Introduction). Example applications of braid groups include knot theory, where any knot may be represented as the closure of certain braids (a result
Braid_group
Natural number
363 = 66, 3-smooth number 46657 = Carmichael number 46972 = number of prime knots with 14 crossings 47058 = primary pseudoperfect number 47160 = 10-th
40,000
Natural number
– super-prime; largest four-digit prime 9988 – number of prime knots with 13 crossings 9999 – Kaprekar number, repdigit There are 112 prime numbers between
9000_(number)
Particular knot energy
energy minimizer in each isotopy class of a prime knot. They also showed the minimum energy of any knot conformation is achieved by a round circle. Conjecturally
Möbius_energy
Link that consists of finitely many unlinked unknots
unlink in Wiktionary, the free dictionary. In the mathematical field of knot theory, an unlink is a link that is equivalent (under ambient isotopy) to
Unlink
American actress
Sumner in the CBS prime time soap opera Knots Landing. McCashin is best known for her role as Laura Avery Sumner on the prime time drama Knots Landing, which
Constance_McCashin
Orientable surface whose boundary is a knot or link
boundary is a given knot or link. Such surfaces can be used to study the properties of the associated knot or link. For example, many knot invariants are most
Seifert_surface
Natural number
is a prime number, a safe prime, a Chen prime, an Eisenstein prime with no imaginary part, an index of a prime Lucas number, and an isolated prime. It
500_(number)
of knot theory, a knot polynomial is a knot invariant in the form of a polynomial whose coefficients encode some of the properties of a given knot. The
Knot_polynomial
American soap opera
Knots Landing is an American primetime television soap opera that aired on CBS from December 27, 1979, to May 13, 1993. A spin-off of Dallas, it was set
Knots_Landing
"Автурханов Умар Джунитович" [Avturkhanov, Umar Dzhunitovich]. Caucasian Knot (in Russian). 26 December 2016. Retrieved 3 April 2024. "Хроника вооруженного
List of leaders of Chechnya (1991–present)
List_of_leaders_of_Chechnya_(1991–present)
American actor and musician (1952–1992)
film A Soldier's Story (1984) and as Frank Williams in the prime-time TV soap opera Knots Landing. Born in Memphis, Tennessee, Riley began acting in high
Larry_Riley_(actor)
Kind of operation in knot theory
field of knot theory, a mutation is an operation on a knot that can produce different knots. Suppose K is a knot given in the form of a knot diagram.
Mutation_(knot_theory)
theorem introduced the theory of hyperbolic 3-manifolds into knot theory and made it of prime importance. In 1982, Thurston received a Fields Medal, the
History_of_knot_theory
Knots Landing is an American prime time television soap opera that aired on CBS from December 27, 1979, to May 13, 1993. The show was created by David
List of Knots Landing characters
List_of_Knots_Landing_characters
German mathematician
published his proof that every oriented knot in S 3 {\displaystyle S^{3}} decomposes as a connect-sum of prime knots in a unique way, up to reordering. After
Horst_Schubert
as knot theory, an invertible knot is a knot that can be continuously deformed to itself, but with its orientation reversed. A non-invertible knot is
Invertible_knot
Normalized hyperbolic volume of the complement of a hyperbolic knot
In the mathematical field of knot theory, the hyperbolic volume of a hyperbolic link is the volume of the link's complement with respect to its complete
Hyperbolic_volume
American mathematician
He gave the first proof of the classical theorem that knots with unknotting number one are prime. He used hard combinatorial arguments for this. Simpler
Martin_Scharlemann
Collection of knots that do not intersect, but may be linked
mathematical knot theory, a link is a collection of knots that do not intersect, but which may be linked (or knotted) together. A knot can be described
Link_(knot_theory)
Vladislav Ardzinba from running for a third term and he instead backed Prime Minister Raul Khadjimba, who also enjoyed support from the Russian authorities
2004 Abkhazian presidential election
2004_Abkhazian_presidential_election
Smallest number of edges of an equivalent polygonal path for a knot
of knots, the stick number is a knot invariant that intuitively gives the smallest number of straight "sticks" stuck end to end needed to form a knot. Specifically
Stick_number
2026 aviation accident in Florida
down at a ground speed of 158 knots (182 mph; 293 km/h). At T-23 seconds, brakes were applied at a speed of 146 knots (168 mph; 270 km/h). At T-19, left
21_Air_Flight_7598
American film and television actor (1943–2020)
Kojak (1973–1978), and as M. Patrick "Mack" MacKenzie in the prime time soap opera Knots Landing (1982–1993). On April 1, 2008, Dobson made his first
Kevin_Dobson
Knot invariant named after Cahit Arf
In the mathematical field of knot theory, the Arf invariant of a knot, named after Cahit Arf, is a knot invariant obtained from a quadratic form associated
Arf_invariant_of_a_knot
beginning of topological knot theory, when polyhedral decompositions were used to compute the homology of covering spaces of knots. Extending to 3 dimensions
Mathematical_visualization
become a teacher, while taking care of his mother and has finally tied the knot. Son of Sardaar In a mid-credits scene, "Po Po Po" is sung and featuring
List of films with post-credits scenes (2010s)
List_of_films_with_post-credits_scenes_(2010s)
Analog of the knot group
In knot theory, an area of mathematics, the link group of a link is an analog of the knot group of a knot. They were described by John Milnor in his Ph
Link_group
travel, tourism, insurance
PRIME KNOT
PRIME KNOT
Male
Italian
Italian and Spanish form of Latin Primus, PRIMO means "first."
Surname or Lastname
German
German : of uncertain origin; possibly from the Latin personal name Primus (‘the first’), borne by several saints; or one composed with a Germanic word meaning ‘to prick or stab’; or from a personal name of Slavic origin Primm, from prēmu ‘right’.French : from a personal name (from Latin Primus).French : nickname from Old French prim ‘first’, possibly given to the eldest child in a family, or alternatively a nickname from Old French and Occitan prim ‘shrewd’, ‘clever’, ‘artful’, ‘sly’.Dutch : variant of Priem.English : variant of Prime.Some of the Prim families in VT descend from a Simon Laval dit Printemps, who was known in English-speaking areas as Seymour Prim.
Boy/Male
Indian, Tamil
Important; Prime
Boy/Male
Indian, Italian, Latin
First Born
Surname or Lastname
English
English : from the Old Norse personal name GrÃmr, which remained popular as a personal name in the form Grim in Anglo-Scandinavian areas well into the 12th century. It was a byname of Woden with the meaning ‘masked person’ or ‘shape-changer’, and may have been bestowed on male children in an attempt to secure the protection of the god. The Continental Germanic cognate grÄ«m was also used as a first element in compound names. Compare Grimaud and Gribble, with the original sense ‘mask’, ‘helmet’. Some examples of the surname may derive from short forms of such names.
Boy/Male
Indian
Prime
Surname or Lastname
English
English : unexplained.Serbian : unexplained.
Girl/Female
Australian, French, German, Italian, Latin, Swedish
First-born
Surname or Lastname
English
English : from a Middle English personal name or nickname. The personal name existed in Old English, and is probably derived from Old English prim ‘early morning’ (from Latin primus ‘first’, used as the name of one of the canonical hours). The surname may be derived from this word as a Middle English nickname in the sense ‘fine’, ‘excellent’.French : feminine form of Prim 3.Dutch : variant of Priem.Probably an Americanized spelling of German Preim, a topographic name (of Slavic origin), perhaps from a river near Hannover; or of Preime, a variant of Primus.
Boy/Male
Arabic, Muslim, Pashtun
Prime Chief
Female
English
English name derived from Latin prima, PRIMULA means "first, prime."
Male
English
English surname transferred to forename use, derived from the Middle English element pris, PRICE means "price" or "prize."Â
Girl/Female
Hindu
Love, Affection
Surname or Lastname
Welsh
Welsh : Anglicized form of Welsh ap Rhys ‘son of Rhys’ (see Reece). This is one of the commonest of Welsh surnames. It has also been established in Ireland since the 14th century, where it is sometimes a variant of Bryson.English : the name is also found very early in parts of England far removed from Welsh influence (e.g. Richard Prys, Essex 1320), and in such cases presumably derives from Middle English, Old French pris ‘price’, ‘prize’, perhaps as a metonymic occupational name for a fixer of prices.Americanized spelling of Jewish Preuss or Preis.
Boy/Male
Hindu, Indian
Chief; Prime
Boy/Male
Welsh American
Son of Rhys.
Girl/Female
Latin
Firstborn.
Boy/Male
Muslim
Prime minister
Boy/Male
Arabic, Muslim
Prime Minister
Boy/Male
Australian, British, Christian, English, Welsh
Son of Rhys; Ardent; Son of the Ardent; Prize
PRIME KNOT
PRIME KNOT
PRIME KNOT
PRIME KNOT
PRIME KNOT
PRIME KNOT
PRIME KNOT
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