this post was submitted on 22 Jan 2024
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Science Memes

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And that is why I don't do statistics (i.imgur.com)
submitted 9 months ago by [email protected] to c/[email protected]
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[–] [email protected] 76 points 9 months ago (1 children)

And if you want to increase accuracy you just add more tests

[–] [email protected] 13 points 9 months ago (1 children)

The failures are probably just flake then

[–] [email protected] 10 points 9 months ago

"prime on my machine"

[–] [email protected] 73 points 9 months ago (1 children)

I wrote an ai that classifies spam emails with 99.9% accuracy.

Our test set contained 1000 emails, 999 aren't spam.

The algorithm:

[–] [email protected] 2 points 9 months ago

Honestly I'd rather have that, than randomly have to miss some important E-mail because the system put it in the junk folder.

[–] [email protected] 60 points 9 months ago (1 children)

All odd numbers are prime: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is experimental error, 11 is prime, and so on, I don't have funding to check all of them, but it suggests an avenue of productive further work.

[–] [email protected] 10 points 9 months ago (1 children)

1 is prime

Them's fightin' words.

[–] [email protected] 6 points 9 months ago

Look, just because it breaks everything, that's no reason not to include it in a joke. We'll just have to rebuild the entire edifice of mathematics.

Seriously, thanks for the link, I hadn't considered the implications of including 1 in the set of primes, and it really does seem to break a lot of ideas.

[–] [email protected] 23 points 9 months ago (3 children)

It's been a fat minute since I last did any programming outside of batch scripts and AHK... I'm struggling to understand how it's not returning false for 100% of the tests

[–] [email protected] 50 points 9 months ago* (last edited 9 months ago)

It is always returning false, but the screen shows a test, where a non-prime evaluating as false is a pass and a prime evaluating as false is a fail :))

[–] [email protected] 27 points 9 months ago (1 children)

The output shown is the result of a test for the function, not the result of the function itself.

[–] [email protected] 12 points 9 months ago

Ooooh I see lol. Thank you!

[–] [email protected] 14 points 9 months ago

It's returning false for all the tests, but it only should be returning false for 95% of them, as 5% are prime.

[–] [email protected] 15 points 9 months ago* (last edited 9 months ago) (2 children)

How many primes are there before 1 and 2^31. IIRC prime numbers get more and more rare as the number increases. I wouldn't be surprised if this would pass 99% of tests if tested with all positive 32 bit integers.

[–] [email protected] 14 points 9 months ago (1 children)

Per the prime number theorem, for large enough N the proportion of primes less than or equal to N is approximately 1/log(N). For N = 2^(31) that's ~0.0465. To get under 1% you'd need N ~ 2^(145).

[–] [email protected] 4 points 9 months ago

So you better use 128-bit unsigned integers 😅

[–] [email protected] 7 points 9 months ago

Wolfram alpha says it's about 4.9%. So 4.9% of numbers in the range 1 to 2^31 are prime. It's more than I expected.

[–] [email protected] 13 points 9 months ago* (last edited 9 months ago) (2 children)

It even passes over 100% of tests!

Edit: I can't read floats.

[–] [email protected] 14 points 9 months ago

have y'all never seen a float before

[–] [email protected] 10 points 9 months ago

The last line reads 95.121 %. I was confused too that it is 121%, but, sadly, no.

[–] [email protected] 11 points 9 months ago* (last edited 9 months ago) (1 children)

Ah yes, my favorite recurring lemmy post! It even has the same incorrect test output.

Last time I saw this I did a few calculations based on comments people made:
https://l.sw0.com/comment/32691 (when are we going to be able to link to comments across instances?)

  • 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.
[–] [email protected] 1 points 9 months ago

But you can use randomised test-cases. Better yet, you can randomise values in test-cases once ~~and throw away the ones you don't like~~ and get arbitrarily close to 100% with a reasonable amount of tests

[–] [email protected] 6 points 9 months ago

why would you store comments in git?

Oh. Oh ha ha ha ha you just don't know 'checkout' from 'check out'. Clean out your desk.