645

Number

$645$ (six hundred and forty-five) is:

$3 \times 5 \times 43$

The $3$rd Poulet number after $341$, $561$:

$2^{645} \equiv 2 \pmod {645}$: $645 = 3 \times 5 \times 43$

The $8$th Fermat pseudoprime to base $4$ after $15$, $85$, $91$, $341$, $435$, $451$, $561$:

$4^{645} \equiv 4 \pmod {645}$

The $9$th heptagonal pyramidal number after $1$, $8$, $26$, $60$, $115$, $196$, $308$, $456$:

$645 = 1 + 7 + 18 + 34 + 55 + 81 + 112 + 148 + 189 = \dfrac {9 \paren {9 + 1} \paren {5 \times 9 - 2} } 6$

The $15$th octagonal number, after $1$, $8$, $21$, $40$, $65$, $96$, $133$, $176$, $225$, $280$, $341$, $408$, $481$, $560$:

$645 = \ds \sum_{k \mathop = 1}^{15} \paren {6 k - 7} = 15 \paren {3 \times 15 - 2}$

The $30$th Smith number after $4$, $22$, $27$, $58$, $\ldots$, $454$, $483$, $517$, $526$, $535$, $562$, $576$, $588$, $627$, $634$, $636$:

$6 + 4 + 5 = 3 + 5 + 4 + 3 = 15$