The following table gives the number of oriented prime alternating links (up to mirror image) by crossing number (down the side) and number of components (across the top).
|
  |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
Total |
|
2 |
0 |
2 |
  |
  |
  |
  |
  |
  |
  |
  |
  |
2 |
|
3 |
1 |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
1 |
|
4 |
1 |
2 |
  |
  |
  |
  |
  |
  |
  |
  |
  |
3 |
|
5 |
2 |
1 |
  |
  |
  |
  |
  |
  |
  |
  |
  |
3 |
|
6 |
3 |
5 |
3 |
  |
  |
  |
  |
  |
  |
  |
  |
11 |
|
7 |
7 |
9 |
2 |
  |
  |
  |
  |
  |
  |
  |
  |
18 |
|
8 |
18 |
24 |
15 |
4 |
  |
  |
  |
  |
  |
  |
  |
61 |
|
9 |
43 |
77 |
30 |
2 |
  |
  |
  |
  |
  |
  |
  |
152 |
|
10 |
144 |
239 |
131 |
41 |
4 |
  |
  |
  |
  |
  |
  |
559 |
|
11 |
490 |
886 |
552 |
83 |
4 |
  |
  |
  |
  |
  |
  |
2,015 |
|
12 |
1926 |
3803 |
2111 |
673 |
93 |
8 |
  |
  |
  |
  |
  |
8,614 |
|
13 |
8139 |
15397 |
10905 |
2683 |
212 |
5 |
  |
  |
  |
  |
  |
37,341 |
|
14 |
34770 |
73150 |
48074 |
14822 |
2512 |
222 |
9 |
  |
  |
  |
  |
173,559 |
|
15 |
159486 |
329254 |
244494 |
81012 |
10688 |
543 |
9 |
  |
  |
  |
  |
825,486 |
|
16 |
730099 |
1595079 |
1216136 |
415167 |
79353 |
8799 |
523 |
18 |
  |
  |
  |
4,045,174 |
|
17 |
3462843 |
7704382 |
6137579 |
2384565 |
447190 |
38387 |
1325 |
12 |
  |
  |
  |
20,176,283 |
|
18 |
16593421 |
37956853 |
32006168 |
12693549 |
2747732 |
360626 |
28629 |
1240 |
23 |
  |
  |
102,388,241 |
|
19 |
80689811 |
190156365 |
164961239 |
71601159 |
16848240 |
2091185 |
128399 |
3252 |
23 |
  |
  |
526,479,673 |
|
20 |
397782507 |
957467036 |
872933793 |
395677877 |
99225494 |
15127802 |
1474139 |
89624 |
2889 |
44 |
  |
2,739,781,205 |
|
21 |
1977282482 |
4894915496 |
4605897871 |
2211591299 |
608018778 |
97277111 |
8769351 |
406766 |
7749 |
34 |
  |
14,404,166,937 |
|
22 |
9941282459 |
25147320994 |
24599611556 |
12428621825 |
3595309394 |
637664644 |
73343721 |
5600130 |
268305 |
6732 |
63 |
76,429,029,823 |
|
23 |
50336761633 |
130481594997 |
131974739093 |
69708724732 |
21685188168 |
4162525590 |
490793689 |
33976610 |
1235305 |
18402 |
63 |
408,875,558,282 |