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.
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?