2821

Number
$2821$ (two thousand, eight hundred and twenty-one) is:


 * $7 \times 13 \times 31$


 * The $5$th Carmichael number after $561$, $1105$, $1729$, $2465$:
 * $\forall a \in \Z: a \perp 2821: a^{2820} \equiv 1 \pmod {2821}$


 * The $9$th Fermat pseudoprime to base $5$ after $4$, $124$, $217$, $561$, $781$, $1541$, $1729$, $1891$:
 * $5^{2821} \equiv 5 \pmod {2821}$


 * The $11$th Poulet number after $341$, $561$, $645$, $1105$, $1387$, $1729$, $1905$, $2047$, $2465$, $2701$:
 * $2^{2821} \equiv 2 \pmod {2821}$: $2821 = 7 \times 13 \times 31$


 * The $14$th Fermat pseudoprime to base $3$ after $91$, $121$, $286$, $671$, $703$, $949$, $1105$, $1541$, $1729$, $1891$, $2465$, $2665$, $2701$:
 * $3^{2821} \equiv 3 \pmod {2821}$


 * The $31$st octagonal number, after $1$, $8$, $21$, $40$, $65$, $\ldots$, $1281$, $1408$, $1541$, $1680$, $1825$, $1976$, $2133$, $2296$, $2465$, $2640$:
 * $2821 = \displaystyle \sum_{k \mathop = 1}^{31} \paren {6 k - 5} = 31 \paren {3 \times 31 - 2}$

Also see