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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