Just for your amusement,
here is a spiral of length 2,957 2,956 primes that crosses just one axis, and hits no
prime on that axis.
I encountered it twice, once in a horizontal orientation (seed: $12+28 i$)
and once in a vertical orientation (seed: $43 + 55 i$).
That it should occur twice is a consequence of the symmetry of the conditions
that render a Gaussian integer prime.
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Just for your amusement,
here is a spiral of length 2,957 primes that crosses just one axis, and hits no
prime on that axis.
I encountered it twice, once in a horizontal orientation (seed: $12+28 i$)
and once in a vertical orientation (seed: $43 + 55 i$).
That it should occur twice is a consequence of the symmetry of the conditions
that render a Gaussian integer prime.
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