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:
$\forall a \in \Z: a \perp 509 \, 033 \, 161: a^{509 \, 033 \, 160} \equiv 1 \pmod {509 \, 033 \, 161}$
$509 \, 033 \, 161 = 1729 \times 294 \, 409$:
$\forall a \in \Z: a \perp 1729: a^{1728} \equiv 1 \pmod {1729}$
$\forall a \in \Z: a \perp 294 \, 409: a^{294 \, 408} \equiv 1 \pmod {294 \, 409}$


Work In Progress
In particular: Work out whether it is the first such product, and if not, establish the list of those
It is the first such product, see OEIS: A207041
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by completing it.
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Also see

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Sources

  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $509,033,161$
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