Prime numbers: Using other number systems

Basicaly our normal number system persists on a very basic sequence:

F(n) = F(n-1) + 1 with a fix basis (Binary, Decimal, Hexadecimal)

But it came to my mind that basicaly prime numbers does not match that criteria very well to identify the nature behind them. As many had tried a sequence in that number system can’t be easily found.

We are used to our Clocks – They have a number system which persists on a 10/60/60/24 system. To calculate in this kind of systems is quite a bit harder as we are used to it. The idea to get a better grip on primes is now to change our usual kind of number system:

For example Fibunacci-Sequence: to a basis of one number
creates: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 while every number is a change of basis

1 1 2 3 5
1 1
2 1 1
2 0 0 1
3 1 0 1
4 1 1 1
4 0 0 2
5 1 0 2
6 1 1 2
3 0 0 0 1

And so on.  As you see the system does not delivers an uniqueness of an normal number system does – the question i like to lock at is: How does a system like above reacts on prime numbers? – because i have the feeling as if the primes have some unique charaterstics in those kind of number systems. As i’m not a full-time mathematician, but i am really keen to discuss this here or via email: jrspam-prime@web-d….de because it looks to me as if nobody has ever thought of changing the number systems on behalf of the prime number problem. Follow up will come…

Prime numbers: Using other number systems