garden/journal/2023-09-29.md

• 29 is drishti in the #Flancia Pattern Language.
• 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 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 because 22 is.
        • 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 7 * 13 * 17.
    • I got to this one by whistling a 1547 tone, seeing it in spectroid, then checking https://anagora.org/prime/1547 :)