619

Number
$619$ (six hundred and nineteen) is:


 * The $114$th prime number


 * The $3$rd after $199$, $409$ of the smallest $10$ primes in arithmetic progression:
 * $619 = 2 \times 210 + 199$


 * The $4$th prime number after $5$, $19$, $101$ of the form $\displaystyle \sum_{k \mathop = 0}^{n - 1} \paren {-1}^k \paren {n - k}!$:
 * $619 = 6! - 5! + 4! - 3! + 2! - 1!$


 * The $2$nd of the $28$th pair of twin primes:
 * $619 - 617 = 2$


 * The $42$nd long period prime after $7$, $17$, $19$, $23$, $29$, $\ldots$, $491$, $499$, $503$, $509$, $541$, $571$, $577$, $593$