661

Number

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

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 $28$th near-repdigit prime after $101$, $113$, $131$, $151$, $\ldots$, $353$, $373$, $383$, $433$, $443$, $449$, $499$, $557$, $577$, $599$

The larger of the $30$th pair of twin primes:

$661 - 659 = 2$