Tunnel number degeneration under the connected sum of prime knots

We study 2-string free tangle decompositions of knots with tunnel number two. As an application, we construct infinitely many counter-examples to a conjecture in the literature stating that the tunnel number of the connected sum of prime knots doesnʼt degenerate by more than one: t(K1#K2)⩾t(K1)+t(K2)−1, for K1 and K2 prime knots.