JackNova Primality Test

By Dario Iacampo
This was one of the very first algorithms I wrote (12/2005) when I started studying programming and C# in particular.
I'm pretty passionate about numbers, in those days I was reading some books about prime numbers and I started searching a different point of view for looking at those numbers.

This is one of the observations I stumbled upon: what is represented here is the remainder of the division of a number for increasingly big numbers.
You can see that the function goes rapidly down for certain values, if it goes to zero you have a perfect divisor for your number but often it goes close to zero but doesn't reach it. To be clear, if you plot the same function for a prime number you get the same behavior but never get a zero for the reminder funcion.

I found that the series of what I called 'Likely Divisors' that are numbers where the function falls down, can be calculated like this:
LDn = LDn-1 - (LDn-1/n)
but each time you choose a number as the more likely divisor, you have to do this test:
calculate remainder for both the flat result of the division and for the next numer: LD + 1;
then pick the one for whom the reminder is the lower and go ahead



Another thing I tried was converting the entire series of prime numbers in binary, represent zeros as empty balls and ones as filled one to have something like a shade that I can watch trying to see something.


But let's go back to my primality test, here it is the algorithm:


Here it is an example of the execution:


Insert an integer
456789
LD_3 -> 152263
LD_43 -> 10623
LD_129 -> 3541
Not a prime number

The algorithm executes the primality test and prints out divisors when finds them.
Here we have that the third, 43° and 129° he tried are divisors.


What makes me think is the part where I choose which is the better divisor to use to test if it divides my number.
There should be some interesting property I'm missing...
In those days I was in University and I shown the algorithm to my math professor, he offered me a couple of theories to look at but that didn't help so much.

I would be glad if anyone of you readers can say if this is an original work or a well known property / rubbish :-)