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):
 * $2310 = 7 \# = 2 \times 3 \times 5 \times 7 \times 11$
 * Hence the smallest positive integer with $5$ distinct prime factors.