Reproduce $e$ to $18,457,734,525,360,901,453,873,570$ decimal places!

Why?

No reason, this is the accidental mathematician category.

Pandigital numbers

Pandigital numbers aren’t that special, it’s a number that has all digits from 1-9, or, 0-9 in it.

For example: 381654729 is a pandigital number (with some extra properties)

Pandigital functions

As Complexity Scientists (and musicians and artists in general) know:

Interesting things will happen when the degrees of freedom available to a system to generate its behaviour, are reduced.

Now, the pandigital constraint can become very interesting when applied to functions, or rather, mathematical operators. The rules are:

  • Take a pandigital number
  • Stick any mathematical operator between any cluster of digits
  • Attempt to get an interesting outcome

Turns out such a pandigital formula is able to approximate the trancendental number \(e\) with uncanny precision!

\[e\approx\left (1 + 9^{-4^{6*7}} \right)^{3^{2^{85}}}\]

It was discovered by Richard Sabey in 2004.

The Numberphile channel has a great video on it:

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