diff --git a/journal/2023-09-29.md b/journal/2023-09-29.md index e5e8a1065..64f23d083 100644 --- a/journal/2023-09-29.md +++ b/journal/2023-09-29.md @@ -1,8 +1,17 @@ - [[29]] is [[drishti]] in the #Flancia [[Pattern Language]]. -- My hobby: think about whether numbers are prime. - - [[209]] is not prime; it is 19 * 11. - - I find this one quite beautiful as there are two simple "proofs" to get there: +- My hobby, sometimes: think about whether numbers are prime while laying down or sitting. + - Take [[209]] -- it is not prime. + - I find this one quite beautiful, this is how I got there: - It is not multiple of two or five trivially. - It is not a multiple of three as its digits don't add up to a multiple. - - It is not a multiple of 7 as 210 is (as 21 is 3 * 7); and it's too near to it. + - It is not a multiple of 7 because 210 is (as 21 is 3 * 7) and it's too near. + - Consider the hypothesis that it is multiple of 11. + - 220 is a multiple of 11. + - 220 - 11 is 209. + - So 209 is a multiple of 11. What is the other factor? + - Consider the hypothesis that it is a multiple of 19. + - 19 * 10 is 190. + - 190 + 19 is 209 precisely, so it is a multiple. + - Therefore 209 is 11 * 19. - [[1547]] is not prime; it is 13 * 7 * 17. + - I don't remember how I got here but it was fun.