Hello guys,

I'll not go deep in my function but i'll explain more later, so, straight to the point:


f(x) = cos(pi(a/x - 0.5))


After a LOT of fatorarions and researchs, i came with this formula, that gives me a 'unique wave' for each number.

Curious facts:

-> The 'wave' goes up and down exact the same number a inputed (x>1),
-> The most impressive: f(x) = 0 only of the intenger dividers of a inputed!
-> We can see that a have (a) numbers that can be divided and results in a integer.

And more properties...


So:

Just looking the f(x)=0 points, i know all dividers of a inputed, and if its only 1 and a itself, its a prime.

for now i think its enough!


Desmos link for easy understanding:
https://www.desmos.com/calculator/fu1ghk5kwa