# Thread: Lower Bound of Density of Primes

1. ## Lower Bound of Density of Primes

Is anyone aware of what the highest lower bound on the density of primes has been proven to be? If high enough, it may prove something major.

2. ## Re: Lower Bound of Density of Primes

As far as I know it's zero, as the primes keep getting spread out further and further and further since as x approaches infinity, 1/log(x) approaches 0.

I mean, we have this (Riemann Hypothesis equivalent) theorem that describes prime number distribution and its relation to the prime number theorem:

And, proven without assumption of the truth of the Riemann Hypothesis, we have this:

Is this what you meant?

3. ## Re: Lower Bound of Density of Primes

Originally Posted by skeptopotamus
Is anyone aware of what the highest lower bound on the density of primes has been proven to be? If high enough, it may prove something major.
It is relatively easy to demonstrate that, given an integer N 'no matter how large', it exists at least an integer M such that none of the numbers M,M+1,...,M+N-1 is prime...

Marry Christmas from Serbia

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