Prime Spiral

$\begin{figure}\begin{center}\BoxedEPSF{prime_spiral.epsf}\end{center}\end{figure}$

The numbers arranged in a Spiral

$\begin{displaymath} \matrix{5 & 4 & 3\cr 6 & 1 & 2\cr 7 & 8 & 9\cr} \end{displaymath}$

with Primes indicated in black, as first drawn by S. Ulam. Unexpected patterns of diagonal lines are apparent in such a plot, as illustrated in the above $199\times 199$ grid.

References

Dewdney, A. K. ``Computer Recreations: How to Pan for Primes in Numerical Gravel.'' Sci. Amer. 259, 120-123, July 1988.

Lane, C. ``Prime Spiral.'' http://www.best.com/~cdl/PrimeSpiralApplet.html.

Weisstein, E. W. ``Prime Spiral.'' Mathematica notebook PrimeSpiral.m.