8321

Number
$8321$ (eight thousand, three hundred and twenty-one) is:


 * $53 \times 157$


 * The $53$rd octagonal number, after $1$, $8$, $21$, $40$, $65$, $\ldots$, $5985$, $6256$, $6533$, $6816$, $7105$, $7400$, $7701$, $8008$:
 * $8321 = \displaystyle \sum_{k \mathop = 1}^{53} \left({6 k - 5}\right) = 53 \left({3 \times 53 - 2}\right)$


 * The $20$th Poulet number after $341$, $561$, $645$, $1105$, $1387$, $1729$, $1905$, $2047$, $2465$, $2701$, $2821$, $3277$, $4033$, $4369$, $4371$, $4681$, $5461$, $6601$, $7957$:
 * $2^{8321} \equiv 2 \pmod {8321}$: $8321 = 53 \times 157$