The first seven terms of a sequence of positive integers are: $$\begin{aligned}
& u _ { 1 } = 15 \\
& u _ { 2 } = 21 \\
& u _ { 3 } = 30 \\
& u _ { 4 } = 37 \\
& u _ { 5 } = 44 \\
& u _ { 6 } = 51 \\
& u _ { 7 } = 59
\end{aligned}$$ Consider the following statement about this sequence: (*) 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 $( * )$ ? A 1 B 2 C 3 D 4 E 5 F 6 G 7
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The first seven terms of a sequence of positive integers are:
$$\begin{aligned}
& u _ { 1 } = 15 \\
& u _ { 2 } = 21 \\
& u _ { 3 } = 30 \\
& u _ { 4 } = 37 \\
& u _ { 5 } = 44 \\
& u _ { 6 } = 51 \\
& u _ { 7 } = 59
\end{aligned}$$
Consider the following statement about this sequence:\\
(*) 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 $( * )$ ?
A 1
B 2\\
C 3\\
D 4
E 5\\
F 6\\
G 7