919

Number
$919$ (nine hundred and nineteen) is:
 * The $157$th prime number.


 * The $4$th and last of the $4$ cubic recurring digital invariants after $55$, $136$, $160$:
 * $919 \to 1459 \to 919$


 * The larger of the $13$th pair of primes whose prime gap is $8$:
 * $919 - 911 = 8$


 * The smaller of the $16$th pair of primes whose prime gap is $10$:
 * $929 - 919 = 10$


 * The $18$th centered hexagonal number after $1$, $7$, $19$, $37$, $61$, $91$, $127$, $169$, $217$, $271$, $331$, $397$, $469$, $547$, $631$, $721$, $817$:
 * $919 = \ds 1 + \sum_{k \mathop = 1}^{18 - 1} 6 k = 18^3 - 17^3$


 * The $19$th palindromic prime:
 * $2$, $3$, $5$, $7$, $11$, $101$, $131$, $151$, $181$, $191$, $313$, $353$, $373$, $383$, $727$, $757$, $787$, $797$, $919$, $\ldots$


 * The $21$st permutable prime after $2$, $3$, $5$, $7$, $11$, $13$, $17$, $31$, $37$, $71$, $73$, $79$, $97$, $113$, $131$, $199$, $311$, $337$, $373$, $733$


 * The $42$nd near-repdigit prime after $101$, $113$, $131$, $151$, $\ldots$, $727$, $733$, $757$, $773$, $787$, $797$, $811$, $877$, $881$, $883$, $887$, $911$

Also see