Swiss primes: This plot shows what I am calling Swiss prime numbers up to 30 million, shown in magenta open circles. I am sure there is a mathematical definition for these prime numbers but I haven't found it yet. They are the prime numbers that are equidistant from their two neighboring primes. In this case, the "loneliness," defined as sqrt(distance_lower * distance_upper) (the geometric mean of separations) is an integer and is equal to the distance from the lower or upper neighboring prime. As you can see from the magenta plot, with a logarithmic x-axis, the loneliness of the Swiss primes also grows faster than log(prime number), as shown by the positive curvature of the envelope of the magneta circles. If you know the proper name for these "Swiss primes" please let me know! See also my previous post:
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