5040/Historical Note

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Historical Note on $5040$

The philosopher Plato decided that the exact number of citizens suitable for his ideal city was $5040$.

His reasons included:

$5040$ has $59$ divisors excluding itself
Can be divided by all numbers from $1$ to $10$ and so can be assembled for various wartime or peacetime collective activities into so many equal teams
Subtracting two hearths (that is, people) from the total, you get $5038$, which is divisible by $11$ as well.
-- Plato's Laws: $738$, $741$, $747$, $771$, $878$


In the science of campanology, a complete sequence of Stedman triples contains $5040$ changes, and takes between $3$ and $4$ hours to accomplish.


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