661

Number
$661$ (six hundred and sixty-one) is:


 * The $121$st prime number


 * The lower end of the $8$th record-breaking gap between twin primes:
 * $809 - 661 = 148$


 * The $15$th integer $n$ after $3$, $4$, $5$, $6$, $7$, $8$, $10$, $15$, $19$, $41$, $59$, $61$, $105$, $160$ such that $m = \ds \sum_{k \mathop = 0}^{n - 1} \paren {-1}^k \paren {n - k}! = n! - \paren {n - 1}! + \paren {n - 2}! - \paren {n - 3}! + \cdots \pm 1$ is prime


 * The $2$nd of the $30$th pair of twin primes:
 * $661 - 659 = 2$