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Need a check on calculating prime distributions for large values

  1. Aug 7, 2013 #1
    My calculator isn't at all happy running the likely hood of finding a prime at 10,000 digits. Since there is a correlation very close to 1/2 the number of primes for each increase of 1000 digits after 1000 digits I was thinking I could just use,

    1/2^(n/1000)×1151.3 = probability of finding a prime for n # of digits

    This doesn't work at all for a small number of digits but I am only concerned about gigantic primes and above. Anyone have an idea to about how many digits this function will be accurate?
     
    Last edited: Aug 7, 2013
  2. jcsd
  3. Aug 7, 2013 #2

    mfb

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    Prime number theorem
    For numbers around a large number N, approximately 1/ln(N) of those numbers are prime.

    For numbers with 10000 digits, the fraction of primes is ##\frac{1}{\ln(10^{10000}) } \approx \frac{1}{23000}##
     
  4. Aug 7, 2013 #3
    Okay so the function I wrote is bunk :)

    Where did I get a calculator that can handle the ln10^10000?
     
  5. Aug 7, 2013 #4

    mfb

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    Staff: Mentor

  6. Aug 7, 2013 #5
    It sure can, thanks for the link!

    Realized that right after I left to get my kids. Brain back-logged :)
     
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