## Prime numbers on my bathroom wall

On popular demand I show here a picture of my bathroom wall.

When we moved into our appartment in 2004 we had to redo our bathroom
completely and I took the opportunity to let beauty of the prime
numbers guide us in the design of one wall.
The construction is the following. Every tile is assigned a positive integer
and primes are red tiles and non-primes are beige.
The numbering is as follows:

The middle tile is number 1, the tile below is 2 and then we continue
in a clockwise spiral

5 6 7

4 1 8

3 2 9

. . 10

giving the color pattern

r b r

b b b

r r b

The tile corresponding to 2 is easily spotted in the picture. Two odd
numbered tiles can never be adjacent and since 2
is the only even prime it is the red tile that is adjacent to two
other red tiles (3 and 11) close to the center of the picture.

Before I decided to use this way of representing the primes, I
experimented with numbering the tiles in a more standard way starting
with 1 in the uppermost left corner

1 2 3 4 5 6 7 8 ...33

34...

But the pattern then became very sensitive to if the line ended at a
prime or a composite number. I much prefer the spiral since it gives a
more canonical representation of the primes. I have also been told,
but I did not know this at the time,

that similar spirals have been
used by early mathematicians in the search for patterns in the
distribution of the prime numbers.

To read more about prime numbers I refer to
wikipedia.

My homepage:

Svante Linusson