2465
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Number
$2465$ (two thousand, four hundred and sixty-five) is:
- $5 \times 17 \times 29$
- The $4$th Carmichael number after $561$, $1105$, $1729$:
- $\forall a \in \Z: a \perp 2465: a^{2464} \equiv 1 \pmod {2465}$
- The $9$th Poulet number after $341$, $561$, $645$, $1105$, $1387$, $1729$, $1905$, $2047$:
- $2^{2465} \equiv 2 \pmod {2465}$: $2465 = 5 \times 17 \times 29$
- The $11$th Fermat pseudoprime to base $3$ after $91$, $121$, $286$, $671$, $703$, $949$, $1105$, $1541$, $1729$, $1891$:
- $3^{2465} \equiv 3 \pmod {2465}$
- The magic constant of a magic square of order $17$, after $1$, $(5)$, $15$, $34$, $\ldots$, $870$, $1105$, $1379$, $1695$, $2056$:
- $2465 = \ds \dfrac 1 {17} \sum_{k \mathop = 1}^{17^2} k = \dfrac {17 \paren {17^2 + 1} } 2$
- The $29$th octagonal number, after $1$, $8$, $21$, $40$, $65$, $\ldots$, $1281$, $1408$, $1541$, $1680$, $1825$, $1976$, $2133$, $2296$:
- $2465 = \ds \sum_{k \mathop = 1}^{29} \paren {6 k - 5} = 29 \paren {3 \times 29 - 2}$
Also see
- Previous ... Next: Carmichael Number
- Previous ... Next: Fermat Pseudoprime to Base 3
- Previous ... Next: Poulet Number
- Previous ... Next: Magic Constant of Magic Square
- Previous ... Next: Octagonal Number
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2465$