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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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