Divisibility rules for ANY number ending in 1, 3, 7 or 9

I have derived formulas for divisibility by ANY number ending in 1, 3, 7 or 9 that can be proven and work EVERY time! In fact, every number has a divisibility rule!

[JordanMetroidManiac]

Your formulas here allow for absolutely any number to be tested for divisibility into any other number! This doesn't really help much with anything outside of number theory, but I'm really excited to see that "some random guy on YouTube" was able to contribute to our understandings of mathematics! Congratulations on your discovery. I know what it feels like to be complimented on my works in math and I hope you feel it too.

[JordanMetroidManiac]

I think this video deserves to be spotlighted on Numberphile or something. If not that then at least get this video some more views. Two and a half years and only 261 views. Sorry for the several comments.

[JordanMetroidManiac]

It would be interesting to see how divisibility tests work in other bases. Probably base 12 makes things easier (than base 10) since it has more factors, so fewer numbers will actually need a divisibility test. In base 10, all sufficiently large numbers that end in 1, 3, 7, or 9 (not counting 0-9 that are multiples of 2 or 5) don’t have any obvious factors. However, in base 12, it’s numbers that end in 1, 5, 7, and “11” (not counting 0-11 that are multiples of 2 or 3) that don’t have any obvious factors. It’s like 12 spans more numbers than 10, but has the same amount of nontrivial numbers for divisibility tests, so there is a greater density of numbers that are easily seen to be divisible by 2, 3, 4, 6, and 12. In base 10, it’s just 2, 5, and 10. This idea of course extends to other bases too. Use superior highly composite numbers for the bases for the best divisibility tests (of which 12 is one, the next one is 60).