Re: Consequence of Prime Number Theorem



It is not quite what you ask, but there is a result, originally due to
Hoheisel,
that for any large x, there is a prime between x an x + x^c. Hoheisel
origianlly got c to be
32/33 or something like that, but I believe it has been lowered to
about 3/5 by various people. Since, if c < 1, (mx)^c < x for large
x's, this is sort of close to what you ask. I have no access to any
library at this time, nor a fast internet connection, but if you
browse and look for "Hoheisel", something should show up.

Sincerely

Vladimir Drobot
http://www.vdrobot.com


On Jan 10, 8:59Êam, Xan <xancor...@xxxxxxxxx> wrote:
Hi,

I know that as a consequence of PNT, we have that:
"For all m>=1, there exists x_0(m) such that for all x>=x_0 there is a
prime number in the interval (mx, (m+1)x)"

I just want to know what is x_0. Or at least a good lower bound of x_0
I tried but the better is that x_0 >= e^(m^2)

Can anyone help me to find more good bound (non-exponential)

Thanks a lot,
Xan.

.