5167

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


 * The $688$th prime number


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