I think I see a pattern. Div by 9: Add the 1s place to the priors. Div. by 11: Subtract the 1s place from the priors. Div by 19: Multiply the 1s place by 2 and add to the priors. Div. by 21: Multiply the 1s place by 2 and sutract from the priors. ... - ThreadSky

elviszap.bsky.social • 80 days ago

I think I see a pattern. Div by 9: Add the 1s place to the priors. Div. by 11: Subtract the 1s place from the priors. Div by 19: Multiply the 1s place by 2 and add to the priors. Div. by 21: Multiply the 1s place by 2 and sutract from the priors. ...

Comments

elviszap.bsky.social•80 days ago

Div by 31: Mult. the 1s place by 3 and sub from the priors. Div by 39: Mult. the 1s place by 4 and add to the priors. Div by 41: Mult. the 1s place by 4 and sub from the priors. Div by 49: Multiply the 1s place by 5 and add to the priors. Div by 51: Multiply the 1s place and sub from the priors.

elviszap.bsky.social•80 days ago

I'll continue in a moment. But note that because of congruences, from 21, 39, 49, and 51 you get tests for 3 and 7, 3 and 13, 7 and 7, and 3 and 17, respectively.

Div. by 59: mult. 1s place by 6 and add to the priors. Div. by 61: mult. 1s place by 6 and sub from priors.

elviszap.bsky.social•80 days ago

Div by 69: mult. 1s place by 7 and add to the priors. Div by 71: mult. 1s place by 7 and sub from the priors. Div. by 79: mult. 1s place by 8 and add to the priors. Div. by 81: mult. 1s place by 8 and sub. from priors. Div by 89: mult. 1s place by 9 and add to the priors. What primes are missing?

elviszap.bsky.social•80 days ago

23,37,43,47,53,67,73,83,& 97. But note we found div'blty tests for some composites as well. So the test for 69 is a test for 23. To test for div by 37, mult. 1s place by 11 and subtract. (What's the test for 109?). Look: 3x43=129. The test for 129 is mult. the last digit by 13 and add to the priors.

elviszap.bsky.social•80 days ago

So that's the test for 43. Meanwhile, 3x47=141. So the test for 43 is the test for 141. Mult. the 1s place by 14 and subtract from the priors. Look at 53. 3x53 is 159. The test for 53 is to multiply the 1s place by 16 and add to the priors. I'll write out the other tests later.

elviszap.bsky.social•80 days ago

I hope you can see WHY they work. The WHY is not far from a proof. I am sure that tons of other people know this and these divisibility tests are "well known facts." That is written in a text book somewhere. A "Well Known Mathematical Fact" is like a famous mathematician. Oxymoronic isn't it.

Comments

Posting Rules

Reply