Maria, I am sceptical that your spirals have any special significance whatsoever. Prime numbers should not be dependent in any particular way on the base system employed. So what would these spirals look like when converted to, say, base 2? Or base 9?

The only thing that could alleviate my specticism would be a proof that base 10 is somehow fundamentally special, and not only a reflection of the number of fingers on our hands. Aaron