0, 1, and negative numbers

You likely noticed I began with 2 rather than 1 or 0 when I first constructed the hexagon. Why?  Because they do not fit inside — they stick off the hexagon like a tail.  Perhaps that’s where they belong.

However, if one makes a significant and interesting assumption, then 1 and 0 fall in their logical locations – in the 1 and 0 cells, respectively.

Let’s consider a few lessons we’ve learned so far that support this new assumption:

  • 2 and 3 are unique primes. They define this system and set the boundary conditions to corral all the other numbers. Unlike all the other prime numbers, they reside outside n or n+2 cells. They rest side-by-side, unlike any other primes. Add them together, and they equal another prime (the next prime and the first n prime) – a unique ability.  I assert, as others have, they are more than twin primes – and, in this hexagon universe, they are conjoined twin primes. I further assert, they are special, and should be handled differently than I have thus far.
  • 0 family (n+1) numbers are even and divisible by 3.  This is true for 0.
  • 1 family (n+2) members are odd, not divisible by three and may be prime.  This is true for 1.

Let’s now reconsider the early construction of the hexagon with this assumption: 2 and 3, because of their conjoined nature, have the same spin.  If this is done, it becomes obvious the number 1, of course, lands in a 1 cell.  0 lands in a 0 cell.

So the hexagon looks like this:

hexagoncolor0and1  Prime Hexagon: 0 through 100.
The Prime Hexagon: 0 through 100

With 0 and 1 integrated into the hexagon so neatly, perhaps negative numbers also fit. They too may be added, but it’s debatable how that logic fits exactly.