Abstract
Let K 1 and K 2 be nontrivial knots in the 3-sphere S 3. In this paper, we show that if the tunnel number of K 1# K 2 is two, then either both tunnel numbers of K 1 and K 2 are one, or one of K 1 and K 2 is a 2-bridge knot and the other's tunnel number is at most two.
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