95.121% accuracy

122 points · 12 comments · view on lemmy.world

12 Comments

vicfic@iusearchlinux.fyi · 19 pts · 3y (1 reply)

Wait till you include floating numbers. "There are an infinite numbe of numbers between any two natural numbers" So technically you could increase that percentage to 99.9999....%

rikudou@lemmings.world · 26 pts · 3y

You don't even need floats for that. Just increase the amount of tests.

Cevilia@lemmy.blahaj.zone · 14 pts · 3y (2 replies)
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smitten@lemmy.blahaj.zone · 6 pts · 3y (1 reply)

Actually it would approach 100% without ignoring data wouldn’t it?

Cevilia@lemmy.blahaj.zone · 2 pts · 3y
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xthexder@l.sw0.com · 10 pts · 3y (4 replies)

A few calculations I did last time I saw this meme (over at !programmer_humor@programming.dev):

  • 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

CommunityLinkFixer@lemmings.world · 4 pts · 3y

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: !programmer_humor@programming.dev

smitten@lemmy.blahaj.zone · 2 pts · 3y (2 replies)

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%)

xthexder@l.sw0.com · 3 pts · 3y (1 reply)

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)

smitten@lemmy.blahaj.zone · 2 pts · 3y

Ah, ok yeah that makes sense.

Haus@kbin.social · 5 pts · 3y

The Sieve of Justafewofthese.

NotAUser@lemmy.blahaj.zone · 5 pts · 3y

By the prime number theorem, if the tests go from 1 to N, the accuracy will be 1 - 1 / ln(N). They should have kept going for better accuracy.

muntoo@lemmy.world · 2 pts · 3y

Aw man, my prime number classifier is only 4.879% accurate. :(