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Distribution of primes

  1. Mar 16, 2009 #1
    Before I went to bed I had an idea about integers. Is there such thing as a prime number density? I just listed 1 through 50 and found that primes aren't uniformly distributed(that I noticed). Now by typical density definition the density should be the number of primes as a function of some bound over the space. Has anyone done work on this?
  2. jcsd
  3. Mar 16, 2009 #2


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    Staff: Mentor

    Look for prime number theorem.
  4. Mar 16, 2009 #3

    matt grime

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    The margin is too small to even begin to list them.
  5. Mar 16, 2009 #4
    But does there exist a relationship that tells us exactly how many primes are within a certain bound?
    Is there some complex pattern?
  6. Mar 16, 2009 #5
    Funny you should say that I just found a remarkable proof of Fermats last theorem but my margin was too small to write it down.Now I have forgotten it.Damm.
  7. Mar 16, 2009 #6
    That's exactly what I said when I sent in my paper to the Clay institute: the margin was too small but the proofs of all seven so called unsolvables are trivial--Do I get my money now?. They didn't take it to well.
  8. Mar 17, 2009 #7


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    It doesn't matter who you are, it'll be safe to say that many people smarter than you have spent the equivalent of many lifetimes of full-time study looking at the distribution of prime numbers.

    Suffice to say that any progress in this area isn't going to come about from empirical study of their distribution.
  9. Mar 17, 2009 #8
  10. Apr 7, 2009 #9
    Actually, the Fourier transform of the distribution of zeros of the zeta at +1/2 is equal to the distribution of primes and prime powers.
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