So now I'm in a debate about whether or not p mod 3, with p an odd
prime greater than 3, is random or not, when I say the result of
marching up the primes is random, like coin flips.
That is crucial for my more political claim that mathematicians wrongly
ignore randomness that can be found with primes.
But hey, maybe I'm wrong, but what does that mean exactly?
Well, I say primes show no preference for a particular residue modulo a
lesser prime, so the behavior is random because no rules are around to
make it not be random.
If I am wrong, then that statement is what is wrong, and primes DO show
some preference modulo a lesser prime.
To understand what that means consider yet again what I showed with the
first 23 primes after 3:
5 mod 3 = 2, 7 mod 3 = 1, 11 mod 3 = 2, 13 mod 3 = 1, 17 mod 3 = 2,
19 mod 3 = 1, 23 mod 3 = 2, 29 mod 3 = 2, 31 mod 3 = 1, 37 mod 3 = 1,
41 mod 3 = 2, 43 mod 3 = 1, 47 mod 3 = 2, 53 mod 3 = 2, 59 mod 3 = 2,
61 mod 3 = 1, 67 mod 3 = 1, 71 mod 3 = 2, 73 mod 3 = 1, 79 mod 3 = 1,
83 mod 3 = 2, 89 mod 3 = 2, 97 mod 3 = 1
So the sequence is
2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1
and if the sequence is random, you can only say that 1 or 2 is next in
the sequence.
In case that doesn't make sense, randomness is about NOT knowing what
is coming next beyond the 50% probability, like with a coin, can you
predict whether it will be heads or tails?
(If you can you can make a lot of money betting people against your
ability.)
If there are no rules so that either possibility is equally likely,
then either possibility can occur.
That is crucial, if I am wrong, then there are rules that slant whether
you get 1 or 2, one way or the other and rules mean PREDICTION is
possible.
So someone might be able to say that after the 321st prime, you are
actually more likely to get 1 than 2, considering p_321 mod 3.
PREDICTION is key here.
If p mod 3 is NOT random, then knowing rules governing the behavior
could allow you to predict, that say, 2 is more likely to be next.
So remember, and this is crucial in this debate, that if I am wrong,
then there are some rules that could help you figure out which
number--1 or 2--would come next in that sequence.
There can be no other way, logically.
My fear, which is why I'm making yet another post, is that too many of
you have been beaten down by the easy tactic that mathematicians and
math people have of simply being abstruse.
If things get complicated, people zone out or fear that they're just
too stupid to get it.
Well let me be the one who looks stupid here. I'll ask the questions
no matter how stupid I look, and notice that people from math circles
have no problems with the put-downs.
And neither do I.
The politics here are HUGE. If I can convince some of you that math
people routinely lie in this area it could be an immense swing.
If I am wrong, then, oh well, I'll learn something myself about primes.
My credibility is not an issue.
Math people have already marked me as a crackpot across the web.
So now you know the stakes. I say math people are vicious and
ruthless, quite capable of lying on a huge scale, and of course, they
would be mad as hornets and ornery as cornered rattlesnakes for that to
come out, so I expect it to get very brutal.
But make no mistake, if p mod 3 is NOT random, then damn it, somebody
better start talking about how you predict the next number in the
sequence beyond saying there is a 50% chance it is 1, or 2.
Concrete tests are CRUCIAL when dealing with intelligent people who
have a lot to lose, and a history of successfully lying to a lot of
people all over the world.
James Harris
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