3610

Number
$3610$ (three thousand, six hundred and ten) is:


 * $2 \times 5 \times 19^2$


 * The $19$th pentagonal pyramidal number after $1$, $6$, $12$, $40$, $75$, $126$, $196$, $288$, $405$, $550$, $726$, $936$, $1183$, $1470$, $1800$, $2176$, $2601$, $3078$:
 * $3610 = \displaystyle \sum_{k \mathop = 1}^{19} \dfrac {k \paren {3 k - 1} } 2 = \dfrac {19^2 \paren {19 + 1} } 2$


 * The $20$th integer $m$ such that $m! - 1$ (its factorial minus $1$) is prime:
 * $3$, $4$, $6$, $7$, $12$, $14$, $30$, $32$, $33$, $38$, $94$, $166$, $324$, $379$, $469$, $546$, $974$, $1963$, $3507$, $3610$