Distribution of prime numbers

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I don't know if anyone has said this (too tired to read the whole thread), but I think that they have thinned down the gap required find a prime. I.E. there is a prime in between n and 1.6n or something like that.


After reading the wikipedia article on Bertrand's Postulate, it appears that for a sufficiently large n, there is a prime between n and (1+a)n for smaller a.
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From what I have heard in various talks and read on Wikipedia, estimating the error term (how far off is the number ln(N) from the actual number of primes below N) is heavily related to the Riemann Hypothesis (the most famous non-solved mathematical problem in modern mathematics).

They are exactly related. If the Riemann hypothesis is true then the difference between Li(x) and the actual number of primes less than x, called pi(x), will never be more than √x * ln x. On the flip side, if the difference between Li(x) and pi(x) was proven to never exceed √x * ln x, it would imply the Riemann hypothesis.
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