397

Number
$397$ (three hundred and ninety-seven) is:


 * The $78$th prime number


 * The $12$th centered hexagonal number after $1$, $7$, $19$, $37$, $61$, $91$, $127$, $169$, $217$, $271$, $331$:
 * $397 = \displaystyle 1 + \sum_{k \mathop = 1}^{12 - 1} 6 k = 12^3 - 11^3$


 * The larger of the $3$rd pair of primes whose prime gap is $8$:
 * $397 - 389 = 8$