Is Prime Number Density Uniformly Distributed Among Integers?

[Winzer]

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?

 

[Borek]

Look for prime number theorem.

 

[matt grime]

Has anyone done work on this?

The margin is too small to even begin to list them.

 

[Winzer]

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?

 

[Dadface]

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.

 

[Winzer]

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.

 

[alxm]

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.

 

[Count Iblis]

http://arxiv.org/abs/0903.2592

 

[riemannzeta]

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.