By way of example, the unknot has crossing number zero, the trefoil knot three and the figure eight knot four. There are no other knots with a crossing number this low and just two knots have crossing number 5, but the number of knots with a particular crossing number increases rapidly as we go higher.

Knots (to be precise prime knots are traditionally indexed by crossing number, with a subscript to indicate which particular knot out of those with this many crossings is meant (this sub-ordering is not based on anything in particular). The listing goes 3_{1} (the trefoil knot), 4_{1} (the figure-eight knot), 5_{1}, 5_{2}, 6_{1}, etc. This order has not changed significantly since P. G. Tait published a tabulation of knots in 1877.