The above is a variation of an Ulam spiral, a square spiral of integers used
by Stanislaw Ulam to visualize and study the distribution of prime numbers.
Ulam indicated primes by black squares as done here; squares representing
composites were left blank. Here, dark and light shades indicate odd and
even composites respectively. Gray squares correspond to ``almost primes''
(products of two distinct primes). Numbers represented by blue have a certain
property, while those shown by yellow, along with primes and almost primes,
do not. As a number puzzle, what is this property?

The visualization is simpler in this graphic focusing on fewer elements, as well as
in this variation of it. Simpler still is one with only the mystery numbers marked,
and another version, both with certain diagonals highlighted.