• @xthexder@l.sw0.com
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    9 months ago

    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

  • VicFic!
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    09 months ago

    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_Sage
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      09 months ago

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