My rediscovery of The Sieve of Eratosthenes

I’ve been playing around with combining the heavenly stems and earthly branches (干支) in numerical form. The ten heavenly stems are represented by digits 0 – 9, while the earthly branches by the digits 0 – eleven, having created special digits for ten and eleven. (See following illustration).

I arranged the combined digits in a circuit like a clock, and then colorized each according to how well they are divisable. See drawing underneath:

I then noticed that the colors were symmetrical mirrored along the 0/60 – 30 line.

Then I saw that the primes were almost symmetrical too! And if I redifined these numbers as ”primes relative to 60”, they were also symmetrical. The definition being: ”those numbers that do not share the same prime factors with 60, i.e. 2, 3, 5”. This means that if x is a ”prime relative to 60” then there is also a y that is a ”prime relative to 60”, such that x+y = 60!

Actually I found out that this was basically because of the ”primes relative to 30 = 2x3x5” were also symmetrical, and that the symmetry would continue for each reiteration of digits. Thus, if x is prime relative to N, then N+x is too!

I even found this true with ”primes relative with 6 = 2×3” and with ”primes relative with 15 = 3×5″. I conjectured that this would be the case even for N = 210 = 2x3x5x7, which would eliminate those numbers divisable with 7.

I then found the following article on The Sieve of Eratosthenes: https://arxiv.org/pdf/1905.03117.pdf

I found out that ”primes relative to 30” are termed ”3-primes”.

I had independently discovered The Sieve of Eratosthenes and the results of the first two theorems in the article, even for a random pick of primes!

Here are two excerpts from the above article that illustrate this:

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