95.121% accuracy
95.121% accuracy
14 comments
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It would be very easy to increase that to 100%, if you're prepared to ignore enough data...
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Actually it would approach 100% without ignoring data wouldn’t it?
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But the only way it would actually get there depends on you, and your willingness to ignore data. :)
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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). Solving99.9995 = 100 - 100 / ln(x)for x givese^200000or7.88 × 10^86858. In other words, the universe will end before any current computer could check that many numbers.
Edit: Fixed community link
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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
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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%)
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The Sieve of Justafewofthese.
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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.
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Aw man, my prime number classifier is only 4.879% accurate. :(
14 comments
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....%
You don't even need floats for that. Just increase the amount of tests.