RE: A mathematical problem I can't seem to get Mathematica to auto solve.
May 21, 2022 at 5:14 pm
(This post was last modified: May 21, 2022 at 5:17 pm by polymath257.)
(May 20, 2022 at 10:01 pm)highdimensionman Wrote: So to find log(n) in a given base then n=b^log(n). so to find log n you find what b has to be to the power too in order for the sum to equal n.
Your wording is confused: it would not be a sum, but a power.
In Mathemtica, the expression is Log[b,n].
Quote:Lets say for the function f1(n) that n=b+1/Powerroot(f1(n),b). So i'm trying to find the root dimension required for the sum to equal n quick.
The only reason I was studying this was because I wanted to see if there was any relationship with prime number distribution.
This seems confused.
In any case, it is known that the n^th prime, p_n is approximately n*Log[n], with the logarithm to the base e in the sense that the limit of the ration is 1 as n goes to infinity. This is related to the Prime Number Theorem (specifically, Rosser's theorem):
https://en.wikipedia.org/wiki/Prime_number_theorem
