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From: Quadibloc on 4 Sep 2008 23:49
On Aug 30, 2:44 pm, Dave Seaman <dsea...(a)no.such.host> wrote:

> You didn't specify a probability distribution on the primes. There is no such
> thing as a uniform probability distribution on a countably infinite set, and
> therefore you must have in mind some nonuniform probability distribution.
> Which one is it?

Good point. "Pick an integer at random" without keeping that point in
mind would yield infinity with probability one, yet infinity isn't an
integer. Which proves by _reductio ad absurdum_ that you're right.
Since any finite integer you pick wold be in an infinitesimally small
group of the very smallest integers - even if 10^(10^(Skewe's Number))
was the number of digits in it.

Thus, if you use a weighted distribution of the integers, you need to
favor the smaller ones. One of the simplest such distributions, if
used to pick a prime, would yield 2 with probability 1/2, 3 with
probability 1/4, 5 with probability 1/8, and so on.

John Savard
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