- cross-posted to:
- mathmemes@lemmy.blahaj.zone
- cross-posted to:
- mathmemes@lemmy.blahaj.zone
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And if you want to increase accuracy you just add more tests
I wrote an ai that classifies spam emails with 99.9% accuracy.
Our test set contained 1000 emails, 999 aren’t spam.
The algorithm:
Honestly I’d rather have that, than randomly have to miss some important E-mail because the system put it in the junk folder.
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.
1 is prime
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.
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
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 :))
The output shown is the result of a test for the function, not the result of the function itself.
Ooooh I see lol. Thank you!
It’s returning false for all the tests, but it only should be returning false for 95% of them, as 5% are prime.
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.
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).
So you better use 128-bit unsigned integers 😅
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.
It even passes over 100% of tests!
Edit: I can’t read floats.
have y’all never seen a float before
The last line reads 95.121 %. I was confused too that it is 121%, but, sadly, no.
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). 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.
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 likeand get arbitrarily close to 100% with a reasonable amount of tests
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.
