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You get e from the primes by averaging the set size of only growing gaps (2,3,5)(7,11)(13,17)... or only non-shrinking gaps (2,3,5,7,11)(13,17)(19,23,29)...

Not a property of primes per se, just a property of growth. It works better with a set of randoms.



I thinking that works for primes because primes are approximately randomly distributed.

But primes are more directly "e" if you look at π(N), the count of primes less than N. That is ~n/ ln(n)

https://en.m.wikipedia.org/wiki/Prime-counting_function


I think that's also another way you can get e from primes.

Can you explain more what you mean by "set size of only growing gaps" - I like this!


(2,3,5) because 2 to 3 = 1 and 3 to 5 = 2. 5 to 7 is also 2 so the gap does not grow, so 7 starts the next set.


Hey that’s cool I like that! Haha :) Thanks for sharing this. You have any GitHub repo or blog talking more about this??? :)


Here're a couple links for you:

https://www.reddit.com/r/math/comments/cbd0a7/found_e_in_the...

https://www.reddit.com/r/math/comments/ikwn03/e_in_the_prime...

https://www.reddit.com/r/math/comments/n0mw3r/deriving_e_fro...




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