5167

Number
$5167$ (five thousand, one hundred and sixty-seven) is:


 * The $688$th prime number


 * The $42$nd centered hexagonal number after $1$, $7$, $19$, $37$, $61$, $91$, $127$, $\ldots$, $2791$, $2977$, $3169$, $3367$, $3571$, $3781$, $3997$, $4219$, $4447$, $4681$, $4921$:
 * $5167 = \ds 1 + \sum_{k \mathop = 1}^{42 - 1} 6 k = 42^3 - 41^3$