The crossing number of knot, denoted as c(K) for a knot diagram K, represents the fewest number of crossings a given knot can have. A diagram of a knot K is known as a minimal diagram of a knot if and only if it has only c(K) crossings.
The crossing number is a powerful tool that can be used in knot tabulation. In fact, a knot is generally tabulated with a number in the form CN, representing the Nth prime knot with a minimum of C crossings. For instance, the trefoil knot below is generally numbered as 31 because it has a minimum of 3 crossings.