garden/journal/2024-07-12.md

• threw 261
  • leading to hex/10 = 271: es todo perfecto como es.
  • I realized hex/6 = 97 is prime, the last I had yet to memorize below 100. That concludes a particular interesting sequence, I guess :)
  • primes:
    • The number of primes below 100 is perhaps interesting to know: 25. So a fourth of the 100 first numbers are prime! Huh.
    • Knowing up to 1000 would unlock getting a statistical feel of how quickly primes 'thin out'.
    • Of course we can also count to 10: 4 primes below 10, so about two fifths.
    • I think they thin out logarithmically but I'm not sure which base, I could look it up but maybe I'll think about it :)
    • It would be cool if it was the natural logarithm. It's the kind of thing that could happen :)
• bluesky:
  • now has an agora bot!
  • it's alpha but it works sometimes (tm)
  • #go at://anagora.bsky.social
    • is that a valid at protocol uri? I believe it sort of should be but I haven't checked :)
• primes:
  • Here I am having counted the primes up to 1000: 168. So down to 16.8% of numbers being prime.
    • The Prime number theorem is what I was inching towards
    • https://en.wikipedia.org/wiki/Prime-counting_function#Table_of_%CF%80(x),_x/log(x),_and_li(x) is a great table
    • The ratio of primes below number n which is exactly 1/#primes_below, can be estimated by 1/(x/log(x))
    • Wow, had I never heard of logarithmic integral function before?
    • So it turns out that li(x) estimates pi(x) better
• I'm going back to Flancia book, and it made me think of what I would in my best dreams try to publish during 2025:
  • A new essay.
  • A book (with publish meant loosely/playfully maybe).
  • A paper.
• paul bricman: straumli ai
  • is down?
• celeste
  • is pretty great