8646

Number
$8646$ (eight thousand, six hundred and forty-six) is:


 * $2 \times 3 \times 11 \times 131$


 * The larger of the $3$rd pair of consecutive positive integers which are each the product of exactly $4$ distinct prime numbers:
 * $8645 = 2 \times 11 \times 13 \times 29$, $8646 = 2 \times 3 \times 11 \times 131$


 * The $66$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $6903$, $7140$, $7381$, $7626$, $7875$, $8128$, $8385$:
 * $8646 = \displaystyle \sum_{k \mathop = 1}^{66} \paren {4 k - 3} = 66 \paren {2 \times 66 - 1}$


 * The $131$st triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $7503$, $7626$, $7750$, $7875$, $8001$, $8128$, $8256$, $8385$, $8515$:
 * $8646 = \displaystyle \sum_{k \mathop = 1}^{131} k = \dfrac {131 \times \paren {131 + 1} } 2$