sentences:  Every non-trivial knot has bridge number at least two, so the knots that minimize the bridge number (other than the unknot) are the 2-bridge knots.It can be shown that every n-bridge knot can be decomposed into two trivial n-tangles and hence 2-bridge knots are rational knots.If K is the connected sum of K1 and K2, then the bridge number of K is one less than the sum of the bridge numbers of K1 and K2.