## 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.