A Knot other than the Unknot which cannot be expressed as a sum of two other Knots, neither of which is unknotted. A Knot which is not prime is called a Composite Knot. It is often possible to combine two prime knots to create two different Composite Knots, depending on the orientation of the two.
There is no known Formula for giving the number of distinct prime knots as a function of the number of crossings. For the first few crossings, the numbers of prime knots are 0, 0, 1, 2, 3, 7, 21, 49, 165, 552, 2176, 9988, ... (Sloane's A002863).
See also Composite Knot, Knot
Sloane, N. J. A. Sequence
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and extended entry in
Sloane, N. J. A. and Plouffe, S.
The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.