Hi emitflesti,
Interesting little exercise indeed. The choice of the base 12 is interesting because 12 is divisible by 2,3,4, and 6 (while 10 is only divisible by 2 and 5, that's why many people use the base 12 for every day calculations).
In any such an arrangement, the multiplication table of a number will draw a spiral because one adds the same number as one rotates around the clock. In the case of this 12-based arrangement, multiplication tables for 2, 3, 4, and 6 form simple pattern because they divide 12. For example, when one adds 4 three times, it comes back to the same spot, hence the triangle for the multiples of 4, and so forth.
Because they do not divide 12, the multiplication tables of 5, 7, and 11 form spirals.
This is a very interesting way to visualize numbers.
If we eliminate the multiples of 4 (blue sectors), of 3 (yellow sectors), and 2 (purple), where we know no prime number can be found, we are left with the red sectors whom equations can be written 12*n+m, where m=1,5,7, or 11, according to the red sector of interest. Numbers in these red sectors do not divide by 2, 3, 6, 12, but in order to be primes, they should also not divide by 5, 7, 11, etc. and these are the exceptions the author of the spiral is talking about.
The problem is, the biggest the number is, the more exceptions are to be checked for.
For example, if we consider the first red sector 12*n+1, which gives 13 25 37 49 61 73 85 97 109 121 133 145 157 169 181 etc. We remove the exceptions of those numbers of this series that divide by 5,7,11,13, we still have numbers in that sector like 289 493 697 901 etc. that can be divided by 17. We then add a new exception with the multiples of 17, and still have numbers that divide by 19, etc. The biggest the series, the more exceptions (spirals=multiplication of smaller prime numbers) and the process is infinite.
So the representation is very interesting, maybe even more so than the Ulam spiral and variations, it still doesn't predict prime numbers in a finite way. OSIT
