  It is conjectured that, on a non-trivial knot in the 3-sphere, no pair of
Dehn surgeries along distinct slopes are purely cosmetic, that is, none of them
yield 3-manifolds those are orientation-preservingly homeomorphic. In this
paper, we show that alternating knots having reduced alternating diagram with
the twist number at least 7, Montesinos knots of length at least 5, and
alternating Montesinos knots of length at least 4 do not admit purely cosmetic
surgeries. As a corollary, we see that large alternating Montesinos knots have
no purely cosmetic surgeries.
