An 
-bridge knot is a knot with bridge
number 
.
The set of 2-bridge knots is identical to the set of rational knots. If 
is a 2-bridge knot, then the BLM/Ho
polynomial 
and Jones polynomial 
satisfy
 |
where 
(Kanenobu and Sumi 1993).
Kanenobu and Sumi also give a table containing the number of distinct 2-bridge knots
of 
crossings for 
to 22, both not counting and counting mirror
images as distinct.
 |  |  |
| 3 | 0 | 0 |
| 4 | 0 | 0 |
| 5 | ||
| 6 | ||
| 7 | ||
| 8 | ||
| 9 | ||
| 10 | 45 | 85 |
| 11 | 91 | 182 |
| 12 | 176 | 341 |
| 13 | 352 | 704 |
| 14 | 693 | 1365 |
| 15 | 1387 | 2774 |
| 16 | 2752 | 5461 |
| 17 | 5504 | 11008 |
| 18 | 10965 | 21845 |
| 19 | 21931 | 43862 |
| 20 | 43776 | 87381 |
| 21 | 87552 | 175104 |
| 22 | 174933 | 349525 |
