469

Number

$469$ (four hundred and sixty-nine) is:

$7 \times 67$

The $13$th centered hexagonal number after $1$, $7$, $19$, $37$, $61$, $91$, $127$, $169$, $217$, $271$, $331$, $397$:

$469 = \ds 1 + \sum_{k \mathop = 1}^{13 - 1} 6 k = 13^3 - 12^3$

The $14$th heptagonal number after $1$, $7$, $18$, $34$, $55$, $81$, $112$, $148$, $189$, $235$, $286$, $342$, $403$:

$469 = \ds \sum_{k \mathop = 1}^{14} \paren {5 k - 4} = \dfrac {14 \paren {5 \times 14 - 3} } 2$

The $15$th integer $m$ such that $m! - 1$ (its factorial minus $1$) is prime:

$3$, $4$, $6$, $7$, $12$, $14$, $30$, $32$, $33$, $38$, $94$, $166$, $324$, $379$, $469$