```Date: Feb 6, 2013 7:12 AM
Author: David Bernier
Subject: number of primes in short interval [a, b] similar to Poisson?

If f: R-> R is a nice, increasing function of t with f(10)>0 (say) andf(t) <= sqrt(t) for t>=10, with f unbounded on [10, oo),and n is some positive integer, a heuristic is that 1/log(n)integers near n are primes.For definiteness, say f(t):= log(t).Let A: n   B:= n + floor( f(n)log(n) ) .Then B-A is about f(n)log(n) and under the heuristic,would contain about  f(n) primes.  Here, f(t):=log(t).So pi(B) - pi(A) ~= log(n) as an approximation, wherepi is the prime counting function.Another heuristic is that the arrival time of primes (time = prime number value) resembles a Poisson process.Then, pi(B) - pi(A) would resemble a Poisson random variable,of parameter  log(n). Mean = Poisson parameter = log(n).I'm interested in large deviations, say 3 sigma or more fromthe mean log(n).In practive, I suppose one could give the values10^9, ... 10^9 + 10^6 - 1 to n and average-out.Have there been numerical experiments comparingpi(B) - pi(A) to a Poisson distribution,or something similar?David Bernier-- dracut:/# lvm vgcfgrestoreFile descriptor 9 (/.console_lock) leaked on lvm invocation. Parent PID 993: sh   Please specify a *single* volume group to restore.
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