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Not according to Wikipedia. At Earth relative to Sun is 42.1 km/s = 94,175 mph. From the sun's surface is 617.5 km/s = 1.38 x 10e6 mph.
Source: https://en.m.wikipedia.org/wiki/Escape_velocity
42.1 km/s is the speed required relative to the sun's surface for objects launching from Earth's surface. You need to look at the value labelled V_te, which is the speed relative to the minor body the object is launching from. In this case, it is 16.6 km/s.