Re: [PrimeNumbers] Prime distribution?
> Consider a continuous list of primes starting 2 ie 2,3,5,7........pNumber of primes between p and p^2 is asymptotically N=2*p^2*log p, so
> and N is the number of primes in the interval >p <p^2
> I've been plotting logN versus logp
> Thus far, I've used data up to p=317.
> This seems to be giving a very good linear fit
> I was wondering whether someone could help to see whether this still holds
> for p>>317.
log N=2log p+log 2+loglog p. So obviously you're going to get a linear
fit, for such a small range. log N increases slightly faster than log p,
but you'd have to plot a much larger range to appreciate the difference.