30,030

Number
$30 \, 030$ (thirty thousand and thirty) is:


 * $2 \times 3 \times 5 \times 7 \times 11 \times 13$


 * The $6$th primorial, after $1$, $2$, $6$, $30$, $210$, $2310$ (counting $1$ as the zeroth):
 * $30 \, 030 = 7 \# = 2 \times 3 \times 5 \times 7 \times 11 \times 13$
 * Hence the smallest positive integer with $6$ distinct prime factors.