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 Picture Alexander– Briggs–Rolfsen Dowker–Thistlethwaite Dowker notation Conway notationcrossinglist Unknot 01 0a1 — —0 Trefoil knot 31 3a1 4 6 2 123:123 Figure-eight knot 41 4a1 4 6 8 2 1234:2143 1231\4324 Cinquefoil knot 51 5a2 6 8 10 2 4 12345:12345 Three-twist knot 52 5a1 4 8 10 2 6 12345:12543 1231\452354 Stevedore knot 61 6a3 4 8 12 10 2 6 123456:216543 1231\45632654 62 knot 62 6a2 4 8 10 12 2 6 123456:234165 1231\45632456 63 knot 63 6a1 4 8 10 2 12 6 123456:236145 1231\45642356

1231\45236456

Seven crossings Picture Alexander–Briggs–Rolfsen Dowker–Thistlethwaite Dowker notation Conway notationcrossinglist 71 7a7 8 10 12 14 2 4 6 1-7:1-7 72 7a4 4 10 14 12 2 8 6 1-7:127-3 73 7a5 6 10 12 14 2 4 8 74 7a6 6 10 12 14 4 2 8 75 7a3 4 10 12 14 2 8 6 76 7a2 4 8 12 2 14 6 10 77 7a1 4 8 10 12 2 14 6 [21112]

Eight crossings Picture Alexander–Briggs–Rolfsen Dowker–Thistlethwaite Dowker notation Conway notation 81 8a­11 4 10 16 14 12 2 8 6 82 8a8 4 10 12 14 16 2 6 8 83 8a­18 6 12 10 16 14 4 2 8 84 8a­17 6 10 12 16 14 4 2 8 85 8a­13 6 8 12 2 14 16 4 10 [3,3,2] 86 8a­10 4 10 14 16 12 2 8 6 87 8a6 4 10 12 14 2 16 6 8 88 8a4 4 8 12 2 16 14 6 10 89 8a­16 6 10 12 14 16 4 2 8 810 8a3 4 8 12 2 14 16 6 10 [3,21,2] 811 8a9 4 10 12 14 16 2 8 6 812 8a5 4 8 14 10 2 16 6 12 813 8a7 4 10 12 14 2 16 8 6 [31112] 814 8a1 4 8 10 14 2 16 6 12 [22112] 815 8a2 4 8 12 2 14 6 16 10 [21,21,2] 816 8a­15 6 8 14 12 4 16 2 10 [.2.20] 817 8a­14 6 8 12 14 4 16 2 10 [.2.2] 818 8a­12 6 8 10 12 14 16 2 4 [8*] 819 8n3 4 8 -12 2 -14 -16 -6 -10 [3,3,2-] 820 8n1 4 8 -12 2 -14 -6 -16 -10 [3,21,2-] 821 8n2 4 8 -12 2 14 -6 16 10 [21,21,2-]

Nine crossings Picture Alexander–Briggs–Rolfsen Dowker–Thistlethwaite Dowker notation Conway notation 91 9a­41 10 12 14 16 18 2 4 6 8 92 9a­27 4 12 18 16 14 2 10 8 6 93 9a­38 8 12 14 16 18 2 4 6 10 94 9a­35 6 12 14 18 16 2 4 10 8 95 9a­36 6 12 14 18 16 4 2 10 8 96 9a­23 4 12 14 16 18 2 10 6 8 97 9a­26 4 12 16 18 14 2 10 8 6 98 9a8 4 8 14 2 18 16 6 12 10 99 9a­33 6 12 14 16 18 2 4 10 8 910 9a­39 8 12 14 16 18 2 6 4 10 911 9a­20 4 10 14 16 12 2 18 6 8 912 9a­22 4 10 16 14 2 18 8 6 12 913 9a­34 6 12 14 16 18 4 2 10 8 914 9a­17 4 10 12 16 14 2 18 8 6 [41112] 915 9a­10 4 8 14 10 2 18 16 6 12 916 9a­25 4 12 16 18 14 2 8 10 6 [3,3,2+] 917 9a­14 4 10 12 14 16 2 6 18 8 [21312] 918 9a­24 4 12 14 16 18 2 10 8 6 919 9a3 4 8 10 14 2 18 16 6 12 [23112] 920 9a­19 4 10 14 16 2 18 8 6 12 [31212] 921 9a­21 4 10 14 16 12 2 18 8 6 [31122] 922 9a2 4 8 10 14 2 16 18 6 12 [211,3,2] 923 9a­16 4 10 12 16 2 8 18 6 14 [22122] 924 9a7 4 8 14 2 16 18 6 12 10 [3,21,2+] 925 9a4 4 8 12 2 16 6 18 10 14 [22,21,2] 926 9a­15 4 10 12 14 16 2 18 8 6 [311112] 927 9a­12 4 10 12 14 2 18 16 6 8 [212112] 928 9a5 4 8 12 2 16 14 6 18 10 [21,21,2+] 929 9a­31 6 10 14 18 4 16 8 2 12 [.2.20.2] 930 9a1 4 8 10 14 2 16 6 18 12 [211,21,2] 931 9a­13 4 10 12 14 2 18 16 8 6 [2111112] 932 9a6 4 8 12 14 2 16 18 10 6 [.21.20] 933 9a­11 4 8 14 12 2 16 18 10 6 [.21.2] 934 9a­28 6 8 10 16 14 18 4 2 12 [8*20] 935 9a­40 8 12 16 14 18 4 2 6 10 [3,3,3] 936 9a9 4 8 14 10 2 16 18 6 12 [22,3,2] 937 9a­18 4 10 14 12 16 2 6 18 8 [3,21,21] 938 9a­30 6 10 14 18 4 16 2 8 12 [.2.2.2] 939 9a­32 6 10 14 18 16 2 8 4 12 [2:2:20] 940 9a­27 6 16 14 12 4 2 18 10 8 [9*] 941 9a­29 6 10 14 12 16 2 18 4 8 [20:20:20] 942 9n4 4 8 10 −14 2 −16 −18 −6 −12 [22,3,2−] 943 9n3 4 8 10 14 2 −16 6 −18 −12 [211,3,2−] 944 9n1 4 8 10 −14 2 −16 −6 −18 −12 [22,21,2−] 945 9n2 4 8 10 −14 2 16 −6 18 12 [211,21,2−] 946 9n5 4 10 −14 −12 −16 2 −6 −18 −8 [3,3,21−] 947 9n7 6 8 10 16 14 −18 4 2 −12 [8*-20] 948 9n6 4 10 −14 −12 16 2 −6 18 8 [21,21,21−] 949 9n8 6 -10 −14 12 −16 −2 18 −4 −8 [−20:−20:−20]

Ten crossings