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Primes Alignment

2023-11-19 | tags : prime numbers, symmetry
Islands of symmetric distribution in prime numbers

Few sequences of gap numbers show a symmetrical distribution.

Within the first 12 millions primes, the largest islands have a span of 11 gap numbers. The following is an example of such islands of gap numbers:

2, 10, 2, 6, 6, 4, 6, 6, 2, 10, 2

and its associated 12 primes:

137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193

prime alignment by inversion and transposition

Symmetry can be visualized by taking the inverted sequence of primes and aligning it to the original sequence. Even numbers (Yellow), Odd numbers (Blue + offset Light-Blue blocks), and primes (Blue + offset Red blocks)


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