Φ²⁸ 60 Stars Astrology: Season Essay Extra: Tanu-chan's Unfinished Obsession Part 2

60stars  Astrology Season  Essay

English  version

By TOKYO-TANUKI

Φ²⁸ 60 Stars Astrology: Season Essay Extra: Tanu-chan's Unfinished Obsession Part 2

1. So, continuing from last time.

I'll write about what Tanu-chan didn't do because I got scared of prime numbers.

Well, the idea that completely solo primes (primes that never become twin primes no matter how many times you add 120) have a 120-period cycle is just Tanu-chan's delusion, but I don't know if there's any pattern to that cycle.

For example, 23 (a solo prime) goes:

23 → 263 (sole prime) → 383 (sole prime) → 503 (sole prime) → 743 (sole prime) → 863 ( solo prime ) → 983 ( solo prime ) → 1103 ( solo prime ) → 1223 ( solo prime ) → 1583 ( solo prime ) → 1823 ( solo prime ) → 2063 ( solo prime )

...and so on, with solo primes continuing. 

But the intervals between them are inconsistent—sometimes 120, sometimes 240, sometimes 360.



I think there's some kind of rhythm to it, but generally, as the numbers get larger, the intervals tend to widen.

For example, 48023 = 120 × (40) + 23 is a perfect solo prime.

After that, it goes:
48023 → 48383 (solo prime) → 48623 (solo prime) → 49103 ( solo prime )

The intervals are roughly 360, 240, and 480.

...But it's not like the intervals suddenly widen dramatically.

By the way, strangely enough, Mersenne primes occur in either the 7 or 31 sequence among prime numbers. 

That is, Mersenne primes lie on the line

7 + 120n

or

31 + 120n

...For example, the Mersenne primes

8191 = 31 + (120 × 68)

2147483647 = 7 + (120 × 17895697)

2305843009213693951

= 31 + (120 × 19215358410114116)

...

7 is a solitary (solo) prime, but 31 belongs to a twin prime group in ZF75.

Why only 7 and 31???

2. Tanu-chan wonders if the world of primes might be like balloons arranged in a mirrored pattern, slowly inflating.

.....It seems a bit different from a spiral🌀.

.....Maybe we could actually observe “Chebyshev's skewness” properly.

Well, this is all just my delusions, though.

..........I thought I'd try writing down all these wild ideas, but I had a scary dream, so I gave up on prime numbers.

If anyone manages to create a good visual of all primes, a good shapes, please tell Tanu-chan secretly!

Tanu-chan💓　TOKYO-TANUKI💛