WTF is this?

The images you see on this blog are output from various Ulam spiral generators I built in Flash, Python and most recently using Arduino. Generally, each dot in an image represents a number with integer 1 at center. In addition to writing algorithms to test each number for primality within a set I have discovered that an infinite number of calculations can be performed to create new designs and animation algorithms. The simplicity and speed of these algorithms make them an ideal fit for embedded systems graphics, scientific, mathematical and artistic explorations.

Tuesday, June 17, 2008

Primes Numbers Beginning With 7

This is a Ulam spiral showing just the primes that begin with 7 (except for the yellow integer 1 at center). So, we have 7, 71, 73, 79 in the center group. The middle ring contains 701, 709, 719, 727, 733, 739, 743, 751, 757, 751, 761, 769, 773, 787, and 797. The outer ring contains 7151, 7159, 7193.... The reason we have squares appearing is fairly obvious. What I find interesting is the distribution of primes within each level. There are notable gaps in the outermost ring. Of course, that ring contains a few thousand numbers so the distribution could appear however we decide to fire off the spiral.

Same idea, this time primes beginning with 2. Notice the deficit of primes in the lower edge of the outer ring.

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