It has been conjectured that the geometric invariant of
knots in 3–space called the width is nearly
additive. That is, letting w(K)∈2N denote the
width of a knot K⊂S3, the conjecture is that
w(K#K')=w(K)+w(K')-2. We give an example of a knot K1
so that for K2 any 2–bridge knot, it appears that
w(K1#K2)=w(K1), contradicting the
conjecture.