across
  • across
How many prime numbers are there between 1,000,000 and 1,100,000?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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mathmate
  • mathmate
Does that have to do with log(n)/n and the Riemann-Zeta function?
mathmate
  • mathmate
Oops, n/log(n)
across
  • across
With this question, I am seeking to clash a mathematical approach with a computerized one. Although it would be interesting to see in how many different ways we can tackle this exercise.

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More answers

mathmate
  • mathmate
So that makes 6692.7, say 6693. Is there a better estimate using R-Z function, I don't really understand it.
across
  • across
mathmate, your approximation is fairly close!
across
  • across
For corroboration, I wrote this: http://ideone.com/qoDbe I am now trying an analytical approach.
mathmate
  • mathmate
Can you elaborate on your analytical approach, or is it proprietary?
mathmate
  • mathmate
6693 wasn't even close, you were being polite! Using the "offset logarithmic integral" \[Li(n) = \int\limits_{2}^{n}\ \frac{dt}{\log(t)}\] I get 7212.99 > 7213. Using your code, I get 7216. So now it's getting close. Also, your code included 1 as a prime, which it is not. This does not change the counts over 1 though.
across
  • across
That made me want to go back and recheck the code. ^^
anonymous
  • anonymous
wow.....
across
  • across
Interesting. Using the logarithmic integral from 2,000,000 to 2,100,000 you get 6881, whereas the (fixed) code chunks out 6871. The error is now negative.
anonymous
  • anonymous
Code looks good except comparison to 1.
anonymous
  • anonymous
btw - why picture change?
mathmate
  • mathmate
I get the same answers, except that I get 6872 for the actual count, both using your code and my code.

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