1541

Number
$1541$ (one thousand, five hundred and forty-one) is:


 * $23 \times 67$


 * The $23$rd octagonal number, after $1$, $8$, $21$, $40$, $65$, $\ldots$, $645$, $736$, $833$, $936$, $1045$, $1160$, $1281$, $1408$:
 * $1541 = \displaystyle \sum_{k \mathop = 1}^{23} \left({6 k - 5}\right) = 23 \left({3 \times 23 - 2}\right)$


 * The $8$th Fermat pseudoprime to base $3$ after $91$, $121$, $286$, $671$, $703$, $949$, $1105$:
 * $3^{1541} \equiv 3 \pmod {1541}$


 * The $6$th Fermat pseudoprime to base $5$ after $4$, $124$, $217$, $561$, $781$:
 * $5^{1541} \equiv 5 \pmod {1541}$