Distribution of primes

  • Thread starter Winzer
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  • #1
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Main Question or Discussion Point

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?
 

Answers and Replies

  • #2
Borek
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Look for prime number theorem.
 
  • #3
matt grime
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Has anyone done work on this?
The margin is too small to even begin to list them.
 
  • #4
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The margin is too small to even begin to list them.
But does there exist a relationship that tells us exactly how many primes are within a certain bound?
Is there some complex pattern?
 
  • #5
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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.
 
  • #6
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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.
 
  • #7
alxm
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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
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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