# 509,033,161

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## Number

$509 \, 033 \, 161$ is:

$7 \times 13 \times 19 \times 37 \times 73 \times 109$

The $472$nd Carmichael number, and one which is the product of $2$ Carmichael numbers:
$\forall a \in \Z: a \perp 509 \, 033 \, 161: a^{509 \, 033 \, 160} \equiv 1 \pmod {509 \, 033 \, 161}$
$509 \, 033 \, 161 = 1729 \times 294 \, 409$:
$\forall a \in \Z: a \perp 1729: a^{1728} \equiv 1 \pmod {1729}$
$\forall a \in \Z: a \perp 294 \, 409: a^{294 \, 408} \equiv 1 \pmod {294 \, 409}$