So why should I keep bugging the sci.physics newsgroup about prime
numbers?

Because mathematicians have done some bizarre crap in this area, and
even dragged physics people into some stuff about prime numbers when
there are these two systems when it comes to understanding the
behavior.

Also, any of you with much training know enough probability and
statistics to not only understand how the prime distribution isn't
random, while other questions like about twin primes are, but you know
there are techniques to determine a random system, which mathematicians
can use to settle the question.

So how could they cheat?

Easy. Claim that such techniques should apply to the prime
distribution itself i.e. the count of primes when it does not, and then
act like that trumps areas where clearly you have randomness like with
where you see twin primes.

Smearing the line between the two systems can allow them to confuse
people indefinitely, unless you know already the answer, and you
figure, hey, these people are going to try to pull something on me.

There are two ways of looking at primes that cover all the ways that
primes express themselves in the natural numbers, where one is rigid
and determined--not at all random--while the other is completely
random.

First I'll show the determined way, which is about the prime
distribution itself--that is, the count of primes.

Well, the count of primes up to a given x is exactly determined by a
simple calculation using the primes up to and including the square root
of x.

For instance, to count the primes up to 24, you need only use

24 - floor(24/2) - floor(24/3) + floor(24/6) + 2 - 1

which is, you subtract the evens, from 24 and then the count of those
divisible by 3, and then you add in those divisible by 6--as they've
been subtracted twice--and then add in 2 for the primes as 2 got
subtracted with the evens and 3 got subtracted with those divisible by
3, and then you subtract one for 1, as one is not prime.

That gives you the EXACT count, and the method is perfect, for any
natural x.

Now then, how many mathematicians this year will apply for grants for
research on twin primes? Or the prime gap? How many papers could be
written in this area?

If you know anything about probability, then see if you can still look
at books mathematicians put out in this area the same way, when you
understand how SIMPLE it is.

James Harris