2026² 60Stars Astrology Season Essay A Happy New Year 2 Isolated (Solo, Single) Primes and Tanu-chan

60stars  Astrology Season  Essay

English  version

By TOKYO-TANUKI

2026²　60 Stars　Astrology　

A Happy New Year 2　

Isolated (Solo, Single) Primes and Tanu-chan

1. So, last time, I explained that twin primes can be grouped into sets of 12.

First, let me reiterate: this blog is made up of Tanu-chan's wild imaginings, so you don't have to believe a word of it!

Anyway, if there are twin primes, I suppose there must be lonely primes too, or isolated primes, or something like that.

For example, 23 isn't a twin prime, but if you keep adding 120 to it:

23 → 143 → 263 → 383 → 503 → 623 → 743......... 

...and while 263, 383, 503, and 743 are prime numbers, they aren't twin primes.

Check today's blog illustration to see! The twin primes are crossed out with red lines, so it's a bit easier to see!



2. So, like this 23, when you keep adding 120, it can become a prime number, but primes that don't form twin primes are called isolated primes or single(solo) primes,maybe.

Tanu-chan observed that candidates for groups similar to the single(solo) primes—specifically, the 23 mentioned earlier and its 120n intervals (referred to as the S23 group)—include the following twelve groups: yes, just at a glance......

S 7
S 23
S 37
S 47
S 53
S 67
S 79
S 83
S 89
S 97
S 113
S 211
........These 12 groups are, for now, the candidates.

Among these, groups like S7, S23, S37, S53, S67, S83, S97, and S113
tend to be solitary most of the time.

Meanwhile, groups like S47, S79, S89, and S211 sometimes become one half of a twin prime pair, sometimes stand alone, and generally looks a little bit lean toward being solitary.

For example, 211

211 + (120 × 3) = 571.

571 is a twin prime with 569:

This twin prime pair is defined by:
4 × 142 + 1 = 569
2 × 285 + 1 = 571

Well, 211 is also related to the ZF25 type of twin primes.

......What's the difference between those that seem unlikely to become one half of a twin prime pair and those that occasionally do?

In other words, difference between

7, 23, 37, 53, 67, 83, 97, 113

and

47, 79, 89, 211


This part is still under research, so I don't know!

......maybe 37+2＋120n＝3k, or something like that.

Well, to put it that way, for example, the twin prime pair 11 and 13:

11 = 2 × 5 + 1
13 = 4 × 3 + 1
so it belongs to the ZF53 group. 

But if we examine its twin, 13, we get:

13→133→253→373→493→613→733→853→973→1093→1213, 

so there are more instances where they are solitary than when they are twins.

This is similar to the solitary primes mentioned earlier—
47, 79, 89, 211—which occasionally become one half of a twin pair.

So, what we can say with certainty is:
① Twin primes come in 12 distinct patterns, 

and

② The solitude of the eight solo primes—namely, 7, 23, 37, 53, 67, 83, 97, and 113—is quite lonesome.

Those with strong solitude, no matter how much 120 is added, will always get caught by a multiple of 3 or 5 (the number in the position to become a twin prime), so they cannot become twin primes.

For example, consider 37:

37 - 157 - 277 - 397 - 517 - 637 - 757 - 877 - 997..........

It becomes prime several times along the way, but it can never become a twin prime. (Probably.)

3. By the way, please note that in Tanu-chan's prime number story, 1, 2, 3, and 5 are not prime numbers.

1, 2, and 5 are numbers that protect the world, so they aren't prime. 5 is actually an even number.

3 might seem like a prime number, but if we counted it as one, even with 120n intervals, they'd all become multiples of 3 (meaning they wouldn't be prime), leaving the group of 3s with just one member.

.....So, even if we included 3 as a prime, it would be all alone, which is why we deliberately didn't group it.



That's all for today.
This was a bit long, wasn't it!




Tanu-chan💓　TOKYO-TANUKI💛