# List of prime knots

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 here for quick comparison of their properties and varied naming schemes.

## Table of prime knots
### Six or fewer crossings

| Name | Alexander– Briggs– Rolfsen | Dowker– Thistlethwaite | Dowker notation | Conway notation | crossinglist |
| Unknot | 0$_1$ | 0a1 | — | — | 0 |
| Trefoil knot | 3$_1$ | 3a1 | 4 6 2 | [3] | 123:123 |
| Figure-eight knot | 4$_1$ | 4a1 | 4 6 8 2 | [22] | 1234:2143 1231\4324 |
| Cinquefoil knot | 5$_1$ | 5a2 | 6 8 10 2 4 | [5] | 12345:12345 |
| Three-twist knot | 5$_2$ | 5a1 | 4 8 10 2 6 | [32] | 12345:12543 1231\452354 |
| Stevedore knot | 6$_1$ | 6a3 | 4 8 12 10 2 6 | [42] | 123456:216543 1231\45632654 |
| 6$_2$ knot | 6$_2$ | 6a2 | 4 8 10 12 2 6 | [312] | 123456:234165 1231\45632456 |
| 6$_3$ knot | 6$_3$ | 6a1 | 4 8 10 2 12 6 | [2112] | 123456:236145 1231\45642356 1231\45236456 |

### Seven crossings

| Alexander– Briggs– Rolfsen | Dowker– Thistlethwaite | Dowker notation | Conway notation | crossinglist |
| 7$_1$ | 7a7 | 8 10 12 14 2 4 6 | [7] | 1-7:1-7 |
| 7$_2$ | 7a4 | 4 10 14 12 2 8 6 | [52] | 1-7:127-3 |
| 7$_3$ | 7a5 | 6 10 12 14 2 4 8 | [43] | |
| 7$_4$ | 7a6 | 6 10 12 14 4 2 8 | [313] | |
| 7$_5$ | 7a3 | 4 10 12 14 2 8 6 | [322] | |
| 7$_6$ | 7a2 | 4 8 12 2 14 6 10 | [2212] | |
| 7$_7$ | 7a1 | 4 8 10 12 2 14 6 | [21112] | |

### Eight crossings

| Alexander– Briggs– Rolfsen | Dowker– Thistlethwaite | Dowker notation | Conway notation |
| 8$_1$ | 8a­11 | 4 10 16 14 12 2 8 6 | [62] |
| 8$_2$ | 8a8 | 4 10 12 14 16 2 6 8 | [512] |
| 8$_3$ | 8a­18 | 6 12 10 16 14 4 2 8 | [44] |
| 8$_4$ | 8a­17 | 6 10 12 16 14 4 2 8 | [413] |
| 8$_5$ | 8a­13 | 6 8 12 2 14 16 4 10 | [3,3,2] |
| 8$_6$ | 8a­10 | 4 10 14 16 12 2 8 6 | [332] |
| 8$_7$ | 8a6 | 4 10 12 14 2 16 6 8 | [4112] |
| 8$_8$ | 8a4 | 4 8 12 2 16 14 6 10 | [2312] |
| 8$_9$ | 8a­16 | 6 10 12 14 16 4 2 8 | [3113] |
| 8$_{10}$ | 8a3 | 4 8 12 2 14 16 6 10 | [3,21,2] |
| 8$_{11}$ | 8a9 | 4 10 12 14 16 2 8 6 | [3212] |
| 8$_{12}$ | 8a5 | 4 8 14 10 2 16 6 12 | [2222] |
| 8$_{13}$ | 8a7 | 4 10 12 14 2 16 8 6 | [31112] |
| 8$_{14}$ | 8a1 | 4 8 10 14 2 16 6 12 | [22112] |
| 8$_{15}$ | 8a2 | 4 8 12 2 14 6 16 10 | [21,21,2] |
| 8$_{16}$ | 8a­15 | 6 8 14 12 4 16 2 10 | [.2.20] |
| 8$_{17}$ | 8a­14 | 6 8 12 14 4 16 2 10 | [.2.2] |
| 8$_{18}$ | 8a­12 | 6 8 10 12 14 16 2 4 | [8*] |
| 8$_{19}$ | 8n3 | 4 8 -12 2 -14 -16 -6 -10 | [3,3,2-] |
| 8$_{20}$ | 8n1 | 4 8 -12 2 -14 -6 -16 -10 | [3,21,2-] |
| 8$_{21}$ | 8n2 | 4 8 -12 2 14 -6 16 10 | [21,21,2-] |

### Nine crossings

| Alexander– Briggs– Rolfsen | Dowker– Thistlethwaite | Dowker notation | Conway notation |
| 9$_1$ | 9a­41 | 10 12 14 16 18 2 4 6 8 | [9] |
| 9$_2$ | 9a­27 | 4 12 18 16 14 2 10 8 6 | [72] |
| 9$_3$ | 9a­38 | 8 12 14 16 18 2 4 6 10 | [63] |
| 9$_4$ | 9a­35 | 6 12 14 18 16 2 4 10 8 | [54] |
| 9$_5$ | 9a­36 | 6 12 14 18 16 4 2 10 8 | [513] |
| 9$_6$ | 9a­23 | 4 12 14 16 18 2 10 6 8 | [522] |
| 9$_7$ | 9a­26 | 4 12 16 18 14 2 10 8 6 | [342] |
| 9$_8$ | 9a8 | 4 8 14 2 18 16 6 12 10 | [2412] |
| 9$_9$ | 9a­33 | 6 12 14 16 18 2 4 10 8 | [423] |
| 9$_{10}$ | 9a­39 | 8 12 14 16 18 2 6 4 10 | [333] |
| 9$_{11}$ | 9a­20 | 4 10 14 16 12 2 18 6 8 | [4122] |
| 9$_{12}$ | 9a­22 | 4 10 16 14 2 18 8 6 12 | [4212] |
| 9$_{13}$ | 9a­34 | 6 12 14 16 18 4 2 10 8 | [3213] |
| 9$_{14}$ | 9a­17 | 4 10 12 16 14 2 18 8 6 | [41112] |
| 9$_{15}$ | 9a­10 | 4 8 14 10 2 18 16 6 12 | [2322] |
| 9$_{16}$ | 9a­25 | 4 12 16 18 14 2 8 10 6 | [3,3,2+] |
| 9$_{17}$ | 9a­14 | 4 10 12 14 16 2 6 18 8 | [21312] |
| 9$_{18}$ | 9a­24 | 4 12 14 16 18 2 10 8 6 | [3222] |
| 9$_{19}$ | 9a3 | 4 8 10 14 2 18 16 6 12 | [23112] |
| 9$_{20}$ | 9a­19 | 4 10 14 16 2 18 8 6 12 | [31212] |
| 9$_{21}$ | 9a­21 | 4 10 14 16 12 2 18 8 6 | [31122] |
| 9$_{22}$ | 9a2 | 4 8 10 14 2 16 18 6 12 | [211,3,2] |
| 9$_{23}$ | 9a­16 | 4 10 12 16 2 8 18 6 14 | [22122] |
| 9$_{24}$ | 9a7 | 4 8 14 2 16 18 6 12 10 | [3,21,2+] |
| 9$_{25}$ | 9a4 | 4 8 12 2 16 6 18 10 14 | [22,21,2] |
| 9$_{26}$ | 9a­15 | 4 10 12 14 16 2 18 8 6 | [311112] |
| 9$_{27}$ | 9a­12 | 4 10 12 14 2 18 16 6 8 | [212112] |
| 9$_{28}$ | 9a5 | 4 8 12 2 16 14 6 18 10 | [21,21,2+] |
| 9$_{29}$ | 9a­31 | 6 10 14 18 4 16 8 2 12 | [.2.20.2] |
| 9$_{30}$ | 9a1 | 4 8 10 14 2 16 6 18 12 | [211,21,2] |
| 9$_{31}$ | 9a­13 | 4 10 12 14 2 18 16 8 6 | [2111112] |
| 9$_{32}$ | 9a6 | 4 8 12 14 2 16 18 10 6 | [.21.20] |
| 9$_{33}$ | 9a­11 | 4 8 14 12 2 16 18 10 6 | [.21.2] |
| 9$_{34}$ | 9a­28 | 6 8 10 16 14 18 4 2 12 | [8*20] |
| 9$_{35}$ | 9a­40 | 8 12 16 14 18 4 2 6 10 | [3,3,3] |
| 9$_{36}$ | 9a9 | 4 8 14 10 2 16 18 6 12 | [22,3,2] |
| 9$_{37}$ | 9a­18 | 4 10 14 12 16 2 6 18 8 | [3,21,21] |
| 9$_{38}$ | 9a­30 | 6 10 14 18 4 16 2 8 12 | [.2.2.2] |
| 9$_{39}$ | 9a­32 | 6 10 14 18 16 2 8 4 12 | [2:2:20] |
| 9$_{40}$ | 9a­27 | 6 16 14 12 4 2 18 10 8 | [9*] |
| 9$_{41}$ | 9a­29 | 6 10 14 12 16 2 18 4 8 | [20:20:20] |
| 9$_{42}$ | 9n4 | 4 8 10 −14 2 −16 −18 −6 −12 | [22,3,2−] |
| 9$_{43}$ | 9n3 | 4 8 10 14 2 −16 6 −18 −12 | [211,3,2−] |
| 9$_{44}$ | 9n1 | 4 8 10 −14 2 −16 −6 −18 −12 | [22,21,2−] |
| 9$_{45}$ | 9n2 | 4 8 10 −14 2 16 −6 18 12 | [211,21,2−] |
| 9$_{46}$ | 9n5 | 4 10 −14 −12 −16 2 −6 −18 −8 | [3,3,21−] |
| 9$_{47}$ | 9n7 | 6 8 10 16 14 −18 4 2 −12 | [8*-20] |
| 9$_{48}$ | 9n6 | 4 10 −14 −12 16 2 −6 18 8 | [21,21,21−] |
| 9$_{49}$ | 9n8 | 6 -10 −14 12 −16 −2 18 −4 −8 | [−20:−20:−20] |

### Ten crossings

| Alexander– Briggs– Rolfsen | Dowker– Thistlethwaite | Dowker notation | Conway notation |
| 10$_1$ | 10a­75 | 4 12 20 18 16 14 2 10 8 6 | [82] |
| 10$_2$ | 10a­59 | 4 12 14 16 18 20 2 6 8 10 | [712] |
| 10$_3$ | 10a­­117 | 6 14 12 20 18 16 4 2 10 8 | [64] |
| 10$_4$ | 10a­­113 | 6 12 14 20 18 16 4 2 10 8 | [613] |
| 10$_5$ | 10a­56 | 4 12 14 16 18 2 20 6 8 10 | [6112] |
| 10$_6$ | 10a­70 | 4 12 16 18 20 14 2 10 6 8 | [532] |
| 10$_7$ | 10a­65 | 4 12 14 18 16 20 2 10 8 6 | [5212] |
| 10$_8$ | 10a­­114 | 6 14 12 16 18 20 4 2 8 10 | [514] |
| 10$_9$ | 10a­­110 | 6 12 14 16 18 20 4 2 8 10 | [5113] |
| 10$_{10}$ | 10a­64 | 4 12 14 18 16 2 20 10 8 6 | [51112] |
| 10$_{11}$ | 10a­­116 | 6 14 12 18 20 16 4 2 10 8 | [433] |
| 10$_{12}$ | 10a­43 | 4 10 14 16 2 20 18 6 8 12 | [4312] |
| 10$_{13}$ | 10a­54 | 4 10 18 16 12 2 20 8 6 14 | [4222] |
| 10$_{14}$ | 10a­33 | 4 10 12 16 18 2 20 6 8 14 | [42112] |
| 10$_{15}$ | 10a­68 | 4 12 16 18 14 2 10 20 6 8 | [4132] |
| 10$_{16}$ | 10a­­115 | 6 14 12 16 18 20 4 2 10 8 | [4123] |
| 10$_{17}$ | 10a­­107 | 6 12 14 16 18 2 4 20 8 10 | [4114] |
| 10$_{18}$ | 10a­63 | 4 12 14 18 16 2 10 20 8 6 | [41122] |
| 10$_{19}$ | 10a­­108 | 6 12 14 16 18 2 4 20 10 8 | [41113] |
| 10$_{20}$ | 10a­74 | 4 12 18 20 16 14 2 10 8 6 | [352] |
| 10$_{21}$ | 10a­60 | 4 12 14 16 18 20 2 6 10 8 | [3412] |
| 10$_{22}$ | 10a­­112 | 6 12 14 18 20 16 4 2 10 8 | [3313] |
| 10$_{23}$ | 10a­57 | 4 12 14 16 18 2 20 6 10 8 | [33112] |
| 10$_{24}$ | 10a­71 | 4 12 16 18 20 14 2 10 8 6 | [3232] |
| 10$_{25}$ | 10a­61 | 4 12 14 16 18 20 2 10 8 6 | [32212] |
| 10$_{26}$ | 10a­­111 | 6 12 14 16 18 20 4 2 10 8 | [32113] |
| 10$_{27}$ | 10a­58 | 4 12 14 16 18 2 20 10 8 6 | [321112] |
| 10$_{28}$ | 10a­44 | 4 10 14 16 2 20 18 8 6 12 | [31312] |
| 10$_{29}$ | 10a­53 | 4 10 16 18 12 2 20 8 6 14 | [31222] |
| 10$_{30}$ | 10a­34 | 4 10 12 16 18 2 20 8 6 14 | [312112] |
| 10$_{31}$ | 10a­69 | 4 12 16 18 14 2 10 20 8 6 | [31132] |
| 10$_{32}$ | 10a­55 | 4 12 14 16 18 2 10 20 8 6 | [311122] |
| 10$_{33}$ | 10a­­109 | 6 12 14 16 18 4 2 20 10 8 | [311113] |
| 10$_{34}$ | 10a­19 | 4 8 14 2 20 18 16 6 12 10 | [2512] |
| 10$_{35}$ | 10a­23 | 4 8 16 10 2 20 18 6 14 12 | [2422] |
| 10$_{36}$ | 10a5 | 4 8 10 16 2 20 18 6 14 12 | [24112] |
| 10$_{37}$ | 10a­49 | 4 10 16 12 2 8 20 18 6 14 | [2332] |
| 10$_{38}$ | 10a­29 | 4 10 12 16 2 8 20 18 6 14 | [23122] |
| 10$_{39}$ | 10a­26 | 4 10 12 14 18 2 6 20 8 16 | [22312] |
| 10$_{40}$ | 10a­30 | 4 10 12 16 2 20 6 18 8 14 | [222112] |
| 10$_{41}$ | 10a­35 | 4 10 12 16 20 2 8 18 6 14 | [221212] |
| 10$_{42}$ | 10a­31 | 4 10 12 16 2 20 8 18 6 14 | [2211112] |
| 10$_{43}$ | 10a­52 | 4 10 16 14 2 20 8 18 6 12 | [212212] |
| 10$_{44}$ | 10a­32 | 4 10 12 16 14 2 20 18 8 6 | [2121112] |
| 10$_{45}$ | 10a­25 | 4 10 12 14 16 2 20 18 8 6 | [21111112] |
| 10$_{46}$ | 10a­81 | 6 8 14 2 16 18 20 4 10 12 | [5,3,2] |
| 10$_{47}$ | 10a­15 | 4 8 14 2 16 18 20 6 10 12 | [5,21,2] |
| 10$_{48}$ | 10a­79 | 6 8 14 2 16 18 4 20 10 12 | [41,3,2] |
| 10$_{49}$ | 10a­13 | 4 8 14 2 16 18 6 20 10 12 | [41,21,2] |
| 10$_{50}$ | 10a­82 | 6 8 14 2 16 18 20 4 12 10 | [32,3,2] |
| 10$_{51}$ | 10a­16 | 4 8 14 2 16 18 20 6 12 10 | [32,21,2] |
| 10$_{52}$ | 10a­80 | 6 8 14 2 16 18 4 20 12 10 | [311,3,2] |
| 10$_{53}$ | 10a­14 | 4 8 14 2 16 18 6 20 12 10 | [311,21,2] |
| 10$_{54}$ | 10a­48 | 4 10 16 12 2 8 18 20 6 14 | [23,3,2] |
| 10$_{55}$ | 10a9 | 4 8 12 2 16 6 20 18 10 14 | [23,21,2] |
| 10$_{56}$ | 10a­28 | 4 10 12 16 2 8 18 20 6 14 | [221,3,2] |
| 10$_{57}$ | 10a6 | 4 8 12 2 14 18 6 20 10 16 | [221,21,2] |
| 10$_{58}$ | 10a­20 | 4 8 14 10 2 18 6 20 12 16 | [22,22,2] |
| 10$_{59}$ | 10a2 | 4 8 10 14 2 18 6 20 12 16 | [22,211,2] |
| 10$_{60}$ | 10a1 | 4 8 10 14 2 16 18 6 20 12 | [211,211,2] |
| 10$_{61}$ | 10a­­123 | 8 10 16 14 2 18 20 6 4 12 | [4,3,3] |
| 10$_{62}$ | 10a­41 | 4 10 14 16 2 18 20 6 8 12 | [4,3,21] |
| 10$_{63}$ | 10a­51 | 4 10 16 14 2 18 8 6 20 12 | [4,21,21] |
| 10$_{64}$ | 10a­­122 | 8 10 14 16 2 18 20 6 4 12 | [31,3,3] |
| 10$_{65}$ | 10a­42 | 4 10 14 16 2 18 20 8 6 12 | [31,3,21] |
| 10$_{66}$ | 10a­40 | 4 10 14 16 2 18 8 6 20 12 | [31,21,21] |
| 10$_{67}$ | 10a­37 | 4 10 14 12 18 2 6 20 8 16 | [22,3,21] |
| 10$_{68}$ | 10a­67 | 4 12 16 14 18 2 20 6 10 8 | [211,3,3] |
| 10$_{69}$ | 10a­38 | 4 10 14 12 18 2 16 6 20 8 | [211,21,21] |
| 10$_{70}$ | 10a­22 | 4 8 16 10 2 18 20 6 14 12 | [22,3,2+] |
| 10$_{71}$ | 10a­10 | 4 8 12 2 18 14 6 20 10 16 | [22,21,2+] |
| 10$_{72}$ | 10a4 | 4 8 10 16 2 18 20 6 14 12 | [211,3,2+] |
| 10$_{73}$ | 10a3 | 4 8 10 14 2 18 16 6 20 12 | [211,21,2+] |
| 10$_{74}$ | 10a­62 | 4 12 14 16 20 18 2 8 6 10 | [3,3,21+] |
| 10$_{75}$ | 10a­27 | 4 10 12 14 18 2 16 6 20 8 | [21,21,21+] |
| 10$_{76}$ | 10a­73 | 4 12 18 20 14 16 2 10 8 6 | [3,3,2++] |
| 10$_{77}$ | 10a­18 | 4 8 14 2 18 20 16 6 12 10 | [3,21,2++] |
| 10$_{78}$ | 10a­17 | 4 8 14 2 18 16 6 12 20 10 | [21,21,2++] |
| 10$_{79}$ | 10a­78 | 6 8 12 2 16 4 18 20 10 14 | [(3,2)(3,2)] |
| 10$_{80}$ | 10a8 | 4 8 12 2 16 6 18 20 10 14 | [(3,2)(21,2)] |
| 10$_{81}$ | 10a7 | 4 8 12 2 16 6 18 10 20 14 | [(21,2)(21,2)] |
| 10$_{82}$ | 10a­83 | 6 8 14 16 4 18 20 2 10 12 | [.4.2] |
| 10$_{83}$ | 10a­84 | 6 8 16 14 4 18 20 2 12 10 | [.31.20] |
| 10$_{84}$ | 10a­50 | 4 10 16 14 2 8 18 20 12 6 | [.22.2] |
| 10$_{85}$ | 10a­86 | 6 8 16 14 4 18 20 2 10 12 | [.4.20] |
| 10$_{86}$ | 10a­87 | 6 8 14 16 4 18 20 2 12 10 | [.31.2] |
| 10$_{87}$ | 10a­39 | 4 10 14 16 2 8 18 20 12 6 | [.22.20] |
| 10$_{88}$ | 10a­11 | 4 8 12 14 2 16 20 18 10 6 | [.21.21] |
| 10$_{89}$ | 10a­21 | 4 8 14 12 2 16 20 18 10 6 | [.21.210] |
| 10$_{90}$ | 10a­92 | 6 10 14 2 16 20 18 8 4 12 | [.3.2.2] |
| 10$_{91}$ | 10a­­106 | 6 10 20 14 16 18 4 8 2 12 | [.3.2.20] |
| 10$_{92}$ | 10a­46 | 4 10 14 18 2 16 8 20 12 6 | [.21.2.20] |
| 10$_{93}$ | 10a­­101 | 6 10 16 20 14 4 18 2 12 8 | [.3.20.2] |
| 10$_{94}$ | 10a­91 | 6 10 14 2 16 18 20 8 4 12 | [.30.2.2] |
| 10$_{95}$ | 10a­47 | 4 10 14 18 2 16 20 8 12 6 | [.210.2.2] |
| 10$_{96}$ | 10a­24 | 4 8 18 12 2 16 20 6 10 14 | [.2.21.2] |
| 10$_{97}$ | 10a­12 | 4 8 12 18 2 16 20 6 10 14 | [.2.210.2] |
| 10$_{98}$ | 10a­96 | 6 10 14 18 2 16 20 4 8 12 | [.2.2.2.20] |
| 10$_{99}$ | 10a­­103 | 6 10 18 14 2 16 20 8 4 12 | [.2.2.20.20] |
| 10$_{100}$ | 10a­­104 | 6 10 18 14 16 4 20 8 2 12 | [3:2:2] |
| 10$_{101}$ | 10a­45 | 4 10 14 18 2 16 6 20 8 12 | [21:2:2] |
| 10$_{102}$ | 10a­97 | 6 10 14 18 16 4 20 2 8 12 | [3:2:20] |
| 10$_{103}$ | 10a­­105 | 6 10 18 16 14 4 20 8 2 12 | [30:2:2] |
| 10$_{104}$ | 10a­­118 | 6 16 12 14 18 4 20 2 8 10 | [3:20:20] |
| 10$_{105}$ | 10a­72 | 4 12 16 20 18 2 8 6 10 14 | [21:20:20] |
| 10$_{106}$ | 10a­95 | 6 10 14 16 18 4 20 2 8 12 | [30:2:20] |
| 10$_{107}$ | 10a­66 | 4 12 16 14 18 2 8 20 10 6 | [210:2:20] |
| 10$_{108}$ | 10a­­119 | 6 16 12 14 18 4 20 2 10 8 | [30:20:20] |
| 10$_{109}$ | 10a­93 | 6 10 14 16 2 18 4 20 8 12 | [2.2.2.2] |
| 10$_{110}$ | 10a­­100 | 6 10 16 20 14 2 18 4 8 12 | [2.2.2.20] |
| 10$_{111}$ | 10a­98 | 6 10 16 14 2 18 8 20 4 12 | [2.2.20.2] |
| 10$_{112}$ | 10a­76 | 6 8 10 14 16 18 20 2 4 12 | [8*3] |
| 10$_{113}$ | 10a­36 | 4 10 14 12 2 16 18 20 8 6 | [8*21] |
| 10$_{114}$ | 10a­77 | 6 8 10 14 16 20 18 2 4 12 | [8*30] |
| 10$_{115}$ | 10a­94 | 6 10 14 16 4 18 2 20 12 8 | [8*20.20] |
| 10$_{116}$ | 10a­­120 | 6 16 18 14 2 4 20 8 10 12 | [8*2:2] |
| 10$_{117}$ | 10a­99 | 6 10 16 14 18 4 20 2 12 8 | [8*2:20] |
| 10$_{118}$ | 10a­88 | 6 8 18 14 16 4 20 2 10 12 | [8*2:.2] |
| 10$_{119}$ | 10a­85 | 6 8 14 18 16 4 20 10 2 12 | [8*2:.20] |
| 10$_{120}$ | 10a­­102 | 6 10 18 12 4 16 20 8 2 14 | [8*20::20] |
| 10$_{121}$ | 10a­90 | 6 10 12 20 18 16 8 2 4 14 | [9*20] |
| 10$_{122}$ | 10a­89 | 6 10 12 14 18 16 20 2 4 8 | [9*.20] |
| 10$_{123}$ | 10a­­121 | 8 10 12 14 16 18 20 2 4 6 | [10*] |
| 10$_{124}$ | 10n­21 | 4 8 -14 2 -16 -18 -20 -6 -10 -12 | [5,3,2-] |
| 10$_{125}$ | 10n­15 | 4 8 14 2 -16 -18 6 -20 -10 -12 | [5,21,2-] |
| 10$_{126}$ | 10n­17 | 4 8 -14 2 -16 -18 -6 -20 -10 -12 | [41,3,2-] |
| 10$_{127}$ | 10n­16 | 4 8 -14 2 16 18 -6 20 10 12 | [41,21,2-] |
| 10$_{128}$ | 10n­22 | 4 8 -14 2 -16 -18 -20 -6 -12 -10 | [32,3,2-] |
| 10$_{129}$ | 10n­18 | 4 8 14 2 -16 -18 6 -20 -12 -10 | [32,21,-2] |
| 10$_{130}$ | 10n­20 | 4 8 -14 2 -16 -18 -6 -20 -12 -10 | [311,3,2-] |
| 10$_{131}$ | 10n­19 | 4 8 -14 2 16 18 -6 20 12 10 | [311,21,2-] |
| 10$_{132}$ | 10n­13 | 4 8 -12 2 -16 -6 -20 -18 -10 -14 | [23,3,2-] |
| 10$_{133}$ | 10n4 | 4 8 12 2 -14 -18 6 -20 -10 -16 | [23,21,2-] |
| 10$_{134}$ | 10n6 | 4 8 -12 2 -14 -18 -6 -20 -10 -16 | [221,3,2-] |
| 10$_{135}$ | 10n5 | 4 8 -12 2 14 18 -6 20 10 16 | [221,21,2-] |
| 10$_{136}$ | 10n3 | 4 8 10 -14 2 -18 -6 -20 -12 -16 | [22,22,2-] |
| 10$_{137}$ | 10n2 | 4 8 10 -14 2 -16 -18 -6 -20 -12 | [22,211,2-] |
| 10$_{138}$ | 10n1 | 4 8 10 -14 2 16 18 -6 20 12 | [211,211,2-] |
| 10$_{139}$ | 10n­27 | 4 10 -14 -16 2 -18 -20 -6 -8 -12 | [4,3,3-] |
| 10$_{140}$ | 10n­29 | 4 10 -14 -16 2 18 20 -8 -6 12 | [4,3,21-] |
| 10$_{141}$ | 10n­25 | 4 10 -14 -16 2 18 -8 -6 20 12 | [4,21,21-] |
| 10$_{142}$ | 10n­30 | 4 10 -14 -16 2 -18 -20 -8 -6 -12 | [31,3,3-] |
| 10$_{143}$ | 10n­26 | 4 10 -14 -16 2 -18 -8 -6 -20 -12 | [31,3,21-] |
| 10$_{144}$ | 10n­28 | 4 10 14 16 2 -18 -20 8 6 -12 | [31,21,21-] |
| 10$_{145}$ | 10n­14 | 4 8 -12 -18 2 -16 -20 -6 -10 -14 | [22,3,3-] |
| 10$_{146}$ | 10n­23 | 4 8 -18 -12 2 -16 -20 -6 -10 -14 | [22,21,21-] |
| 10$_{147}$ | 10n­24 | 4 10 -14 12 2 16 18 -20 8 -6 | [211,3,21-] |
| 10$_{148}$ | 10n­12 | 4 8 -12 2 -16 -6 -18 -20 -10 -14 | [(3,2)(3,2-)] |
| 10$_{149}$ | 10n­11 | 4 8 -12 2 16 -6 18 20 10 14 | [(3,2)(21,2-)] |
| 10$_{150}$ | 10n9 | 4 8 -12 2 -16 -6 -18 -10 -20 -14 | [(21,2)(3,2-)] |
| 10$_{151}$ | 10n8 | 4 8 -12 2 16 -6 18 10 20 14 | [(21,2)(21,2-)] |
| 10$_{152}$ | 10n­36 | 6 8 12 2 -16 4 -18 -20 -10 -14 | [(3,2)-(3,2)] |
| 10$_{153}$ | 10n­10 | 4 8 12 2 -16 6 -18 -20 -10 -14 | [(3,2)-(21,2)] |
| 10$_{154}$ | 10n7 | 4 8 12 2 -16 6 -18 -10 -20 -14 | [(21,2)-(21,2)] |
| 10$_{155}$ | 10n­39 | 6 10 14 16 18 4 -20 2 8 -12 | [-3:2:2] |
| 10$_{156}$ | 10n­32 | 4 12 16 -14 18 2 -8 20 10 6 | [-3:2:20] |
| 10$_{157}$ | 10n­42 | 6 -10 -18 14 -2 -16 20 8 -4 12 | [-3:20:20] |
| 10$_{158}$ | 10n­41 | 6 -10 -16 14 -2 -18 8 20 -4 -12 | [-30:2:2] |
| 10$_{159}$ | 10n­34 | 6 8 10 14 16 -18 -20 2 4 -12 | [-30:2:20] |
| 10$_{160}$ | 10n­33 | 4 12 -16 -14 -18 2 -8 -20 -10 -6 | [-30:20:20] |
| 10$_{161}$ | 10n­31 | 4 12 -16 14 -18 2 8 -20 -10 -6 | [3:-20:-20] |
| 10$_{162}$ | 10n­40 | 6 10 14 18 16 4 -20 2 8 -12 | [-30:-20:-20] |
| 10$_{163}$ | 10n­35 | 6 8 10 14 16 -20 -18 2 4 -12 | [8*-30] |
| 10$_{164}$ | 10n­38 | 6 -10 -12 14 -18 -16 20 -2 -4 -8 | [8*2:-20] |
| 10$_{165}$ | 10n­37 | 6 8 14 18 16 4 -20 10 2 -12 | [8*2:.-20] |

### Higher

* Conway knot 11n34
* Kinoshita–Terasaka knot 11n42

## Table of prime links
### Eight or fewer crossings

| Name | Alexander– Briggs– Rolfsen | Dowker– Thistlethwaite | Dowker notation | Conway notation |
| Unlink | 0$^2$ $_1$ | — | — | — |
| Hopf link | 2$^2$ $_1$ | L2a1 | — | [2] |
| Solomon's knot | 4$^2$ $_1$ | L4a1 | — | [4] |
| Whitehead link | 5$^2$ $_1$ | L5a1 | — | [212] |
| L6a1 | 6$^2$ $_3$ | L6a1 | — | — |
| L6a2 | 6$^2$ $_2$ | L6a2 | — | — |
| L6a3 | 6$^2$ $_1$ | L6a3 | — | — |
| Borromean rings | 6$^3$ $_2$ | L6a4 | — | [.1] |
| L6a5 | 6$^3$ $_1$ | L6a5 | — | — |
| L6n1 | 6$^3$ $_3$ | L6n1 | — | — |
| L7a1 | 7$^2$ $_6$ | L7a1 | — | — |
| L7a2 | 7$^2$ $_5$ | L7a2 | — | — |
| L7a3 | 7$^2$ $_4$ | L7a3 | — | — |
| L7a4 | 7$^2$ $_3$ | L7a4 | — | — |
| L7a5 | 7$^2$ $_2$ | L7a5 | — | — |
| L7a6 | 7$^2$ $_1$ | L7a6 | — | — |
| L7a7 | 7$^3$ $_1$ | L7a7 | — | — |
| L7n1 | 7$^2$ $_7$ | L7n1 | — | — |
| L7n2 | 7$^2$ $_8$ | L7n2 | (6,-8|-10,12,-14,2,-4) | — |

### Higher

| Picture | Alexander– Briggs– Rolfsen | Dowker– Thistlethwaite | Dowker notation | Conway notation |
| | 8$^2$ $_1$ | L8a14 | — | — |
| | — | L10a140 | — | [.3:30] |