631

Number
$631$ (six hundred and thirty-one) is:


 * The $115$th prime number


 * The $15$th centered hexagonal number after $1$, $7$, $19$, $37$, $61$, $91$, $127$, $169$, $217$, $271$, $331$, $397$, $469$, $547$:
 * $631 = \displaystyle 1 + \sum_{k \mathop = 1}^{15 - 1} 6 k = 15^3 - 14^3$


 * The smaller of the $10$th pair of primes whose prime gap is $10$:
 * $641 - 631 = 10$