The first seven terms of a sequence of positive integers are: $u_1=15$ $u_2=21$ $u_3=30$ $u_4=37$ $u_5=44$ $u_6=51$ $u_7=59$

Consider the following statement about this sequence: > $(\ast )$ *If* $n$ is a prime number, *then* $u_n$ is a multiple of 3 *or* $u_n$ is a multiple of 5.

What is the smallest value of $n$ that provides a counterexample to $(\ast )$?

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