2310

Number
$2310$ (two thousand, three hundred and ten) is:


 * $2 \times 3 \times 5 \times 7 \times 11$


 * The $5$th primorial, after $1$, $2$, $6$, $30$, $210$ (counting $1$ as the zeroth):
 * $2310 = 11 \# = 2 \times 3 \times 5 \times 7 \times 11$
 * Hence the smallest positive integer with $5$ distinct prime factors.