Distribution of primes

**Winzer** · Mar16-09, 05:02 AM

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** · Mar16-09, 05:04 AM

Look for prime number theorem.

**matt grime** · Mar16-09, 05:14 AM

Originally Posted by Winzer

Has anyone done work on this?

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

**Winzer** · Mar16-09, 06:21 AM

Originally Posted by matt grime

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** · Mar16-09, 06:22 AM

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** · Mar16-09, 06:27 AM

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** · Mar17-09, 07:30 AM

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** · Mar17-09, 03:23 PM

http://arxiv.org/abs/0903.2592

**riemannzeta** · Apr7-09, 10:06 PM

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.