Re: question about RH

In article
<28790266.1217971498455.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
daniel t <daniel6874@xxxxxxxxx> wrote:

I recall reading that if there's a prime between any two consecutive squares
this implies RH. Is there any reason (like a counterexample--I computed it to
n->10,000) to doubt that there is a prime between (n^2) and (n^2 + n)? It
cuts the interval down brutally but is it empirically implausible?

There is no reason at all to doubt that there's a prime between n^2
and n^2 + n. In fact, it is believed that for all sufficiently large n
there's a prime between n^2 and n^2 + the 17th root of n,
where 17 is a variable. I think it's conjectured that for all
sufficiently large n there's a prime between n and n + (log n)^2.
RH gives very weak information on gaps between primes.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

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