e

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. {{% alert note %}} For example: 381654729 is a pandigital number (with some extra properties) {{% /alert %}} 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: