A prime link is a link that is not a splittable link and for which every representation as a knot sum has an unknot as one of its factors (Hoste 2005). Doll and Hoste (1991) list polynomials for oriented links of nine or fewer crossings, and Rolfsen (1976) gives a table of links with small numbers of components and crossings.
The following table summarizes the number of distinct prime 
-component links having specified
crossing numbers, with no assigned orientations
and with mirror images counted as a single link type.
| components | OEIS | prime  -component links with 1, 2, ... crossings |
| 1 | A002863 | 0, 0, 1, 1, 2, 3, 7, 21, 49, 165, 552, ... |
| 2 | A048952 | 0, 1, 0, 1, 1, 3, 8, 16, 61, 185, 638, ... |
| 3 | A048953 | 0, 0, 0, 0, 0, 3, 1, 10, 21, 74, 329, ... |
| 4 | A087071 | 0, 0, 0, 0, 0, 0, 0, 3, 1, 25, 39, ... |
| 5 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, ... | |
| total | A086771 | 0, 1, 1, 2, 3, 9, 16, 50, 132, 452, 1559, ... |
The following table lists some named links. The notation and ordering follows that of Rolfsen (1976), where 
denotes the 
th
-component link with link
crossing number 
.
| link number | name |
 | unlink |
 | Hopf link |
 | Whitehead link |
 | Borromean rings |
A listing of the first few simple links follows, arranged by link crossing number.
01
01
01
01
01 02 03
01 02 03 04 05 06 07 08
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
01 02 03
01
01 02 03 04 05 06 07 08 09 10
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21
01 02 03
01
