To mathematicians: Why does a 9 appear between prime numbers?

I have treated numbers as 0 or 1. If a number is prime, I have assigned a black circle and if it is not prime, I have put a white circle instead. A green circle is like a white circle, but accompanied of 8 more, that is, they are 9 no primes together. Is it not odd that the number or white circles together or black circles together always are prime numbers, except there are 9 white circles together?  For example there are 3 white circles together, 3 is prime. There are 5 white circles together, 5 is prime. There are 11 white circles together, 11 is prime. There a 13 white circles together, 13 is prime. But 9 white circles together and 9 is divisible by 3.

There are also black circles together but there are 1 together or prime quantities like 3 in this sample. I have not seen prime numbers treated as bits and I think this 9 no prime number can be a hint to unravel the mystery of prime numbers. What function performs a no prime number different of 1 between prime numbers?

Further investigation: check if this pattern goes on with larger numbers. Represent prime numbers in its equivalent in binary and search for new patterns.