Distribution of primes

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

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

Winzer

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.