Re: Digest Number 1753

Danterosati wrote:

> For example, the number of primes appearing in each of the first few
> octaves is:
[snip]
> any comments or pointers to info would be appreciated!

Hi Dante - what you posted is sequence A036378 here:

http://www.research.att.com/~njas/sequences/A036378

I don't think much is known about these prime distributions - mathematicians can't even prove Legendre's conjecture that there's always a prime between n^2 and (n+1)^2. The related sequence A007053 was "computed with Meissel-Lehmer-Legendre inclusion exclusion formula", whatever that means.

--Jon

--- In tuning-math@yahoogroups.com, Jon Wild <wild@...> wrote:

> I don't think much is known about these prime distributions -
> mathematicians can't even prove Legendre's conjecture that there's
always
> a prime between n^2 and (n+1)^2.

Assuming the Riemann hypothesis, they can prove there is always one
between n^3 and (n+1)^3.