this post was submitted on 08 Jul 2023
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Math Memes

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Memes related to mathematics.

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1: Memes must be related to mathematics in some way.
2: No bigotry of any kind.

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95.121% accuracy (i.imgur.com)
submitted 1 year ago by [email protected] to c/[email protected]
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[–] [email protected] 9 points 1 year ago* (last edited 1 year ago) (2 children)

A few calculations I did last time I saw this meme (over at [email protected]):

  • There are 9592 prime numbers less than 100,000. Assuming the test suite only tests numbers 1-99999, the accuracy should actually be only 90.408%, not 95.121%
  • The 1 trillionth prime number is 29,996,224,275,833. This would mean even the first 29 trillion primes would only get you to 96.667% accuracy.

In response to the question of how long it would take to round up to 100%:

  • The density of primes can be approximated using the Prime Number Theorem: 1/ln(x). Solving 99.9995 = 100 - 100 / ln(x) for x gives e^200000 or 7.88 × 10^86858. In other words, the universe will end before any current computer could check that many numbers.

Edit: Fixed community link

[–] [email protected] 4 points 1 year ago

Hi there! Looks like you linked to a Lemmy community using a URL instead of its name, which doesn't work well for people on different instances. Try fixing it like this: [email protected]

[–] [email protected] 2 points 1 year ago (1 children)

I think a more concise answer to the second one would be; it depends on where you decide to round, but as you run it, it approaches 100%, or 99.99 repeating (which is 100%)

[–] [email protected] 3 points 1 year ago (1 children)

The screenshot displays 3 decimal places, which is the the precision I used. As it turns out, even just rounding to the nearest integer still requires checking more numbers than we even have the primes enumerated for (e^200 or 7x10^86)

[–] [email protected] 2 points 1 year ago

Ah, ok yeah that makes sense.