Years ago I noticed that you could consider twin primes probability in
a fairly simple way by assuming that primes have no preferred residue
modulo each other, which gives a nice little formula:
prob = ((p_j - 2)/(p_j -1))*((p_{j-1} - 2)/(p_{j-1} - 1))*...*(1/2)
where you look at the interval p_{j-1}^2 to p_j^2, as my simple idea
was to use the actual count of primes WITHIN that interval with the
prob calculation, so it keeps shifting, as you go higher, you get more
primes, and my simplification works rather well.
THAT is ALL from over 3 1/2 years ago. I pushed the idea further back
then, realized you should be able to do something similar for prime
gaps of arbitrary even size, and realized some depressing things. If
true, my simple idea PROVED the twins prime conjecture and DISPROVED
Goldbach's Conjecture. But in a probabilistic proof!
All that is from over 3 1/2 years ago. I argued about a few things on
Usenet and wandered off, and recently brought the subject up again and
decided I had an axiom which I called the prime residue axiom.
Arguments erupted and posters argued both sides: some claimed I
didn't have an axiom, others claimed that what I had was already
proven but so what?
Oh, and I forgot, you can also find ((p_j - 2)/(p_j -1))*((p_{j-1} -
2)/(p_{j-1} - 1))*...*(1/2), in the twin primes constant!
See: http://mathworld.wolfram.com/TwinPrimesConstant.html
Now I know how people can ignore bold facts like seeing a formula from
a probabilistic interpretation in established literature, which does a
rather good job of predicting twin primes probability with a simpler
formula than what is currently taught, and argue BOTH SIDES as if it
were nothing at all!
People can in fact confidently proclaim that 2+2=5 and believe it, if
you understand human nature and how the mind works.
So there is no doubt that this approach is a simplification, it ties
in easily with prior known research, and has scary implications like
that you can prove the Twin Primes Conjecture and disprove Goldbach's
Conjecture with one interpretation.
But you may have noticed that the math world isn't exactly buzzing
with the news!
If you know your math history you know that study of twin primes got
big about the time I say a rather remarkable error entered into the
mathematical field, where I've proven that the ring of algebraic
integers can be trivially shown to contradict with the field of
complex numbers!
That allows you to appear to prove things without having actually done
so, and as it has been in the field for over a hundred years it has
selected people who are tolerant of the error.
Such people can believe two different and contradictory things at the
same time.
The mathematical flaw at the heart of established number theory
SELECTS such people, as people who are not so capable could not be
number theorists WITH THAT FLAW.
That is, if you were not a person with that peculiar ability, even if
you did not understand that something was wrong with the ring of
algebraic integers thoroughly, you might have some weird feeling that
would push you into a different field, like topology.
Ok, so back to prime numbers! Turns out I have multiple results
around prime numbers. The people who can believe two different and
contradictory things always say that none of them are important! The
prime residue axiom though leads to a prime gap equation. It took me
a while to get that correct but I think I have the correct equation as
of now on my math blog (though I haven't posted it on Usenet, having
put up flawed prior versions).
So why not just use the prime gap equation over a wide range to prove
I'm right?
Because it won't matter to the people who can believe two different
and contradictory things at the same time, who have been selected into
number theory by the core error I found, which means they cannot be
moved by mathematical proof, as given ANY proof they can believe it's
opposite just as easily as believe in the proof itself. Damn
inconvenient, eh?
It's a conundrum. These people dominate number theory because the
error dominates number theory.
I assure you they are special people whose brains allow them to
believe two different and contradictory things at the same time.
The error that entered into number theory over a hundred years ago is
perfect for these type of people and they found a comfortable home in
number theory and fashioned "pure math" to secure that home. Notice
'pure math" came into the field at about the time of the error and at
about the time that the twin primes conjecture was made.
To themselves they are normal!!!
You will NOT get anywhere trying to explain to them that it's not
normal to be able to believe two opposite and contradictory things at
the same time, as their brains work that way. To them it's as natural
as breathing.
The situation is actually kind of fascinating in many ways. God only
knows what can break the hold of these people on number theory. But I
assure you that facts and therefore mathematical proof, cannot.
James Harris
Sounds very gentlemanly, literary and grammatical. But I can't
understand one thing: do you have a proof of the Twin Prime Conjecture
or not?
If yes - where is it?
If no - what's stopping you?
I am confused.
<snip>
> Years ago I noticed that you could consider twin primes probability in
> a fairly simple way by assuming that primes have no preferred residue
> modulo each other
If you make incorrect assumptions you can make a lot of things
simple. In this case you assume "have no preferred residue
modulo each other" means the residues are independent. They
are not.
- William Hughes
NPD Detection = ratio of self referencing words to total unique words. Over
5% indicated high NPD
I, me, mine, my,.....
23+2= 25
25/356 = 7.02%
JSH still narcissistic, but not as bad as usual, unless he is projecting
again- where we should count the "you"s as well or a proportion of them
http://narcissistic-personality.suite101.com/article.cfm/narcissistic_disorder_diagnosis
However, I do believe this set of words below can be reassembled into
something more meaningful to you, me, the planet, and also dramatically
reduce *Vegetable Abuse* which is currently rampant throughout the world.
Unique words:356 Total words:955
Freq. Word
41 THE
27 THAT
25 AND
23 I
21 TO
20 YOU
19 A
16 OF
16 IT
13 WITH
13 PEOPLE
13 AS
11 CAN
11 IN
10 J
10 P
9 PRIME
9 AT
9 PRIMES
8 IS
8 THINGS
8 BELIEVE
8 NUMBER
7 HAVE
7 SO
7 TIME
7 YEARS
7 THEORY
7 NOT
6 BE
6 IF
6 S
6 MATH
6 TWIN
6 ERROR
6 BUT
6 MATHEMATICAL
6 PROOF
5 AXIOM
5 OVER
5 WHICH
5 T
5 CONJECTURE
5 THEM
5 WAS
5 FOR
5 AGO
5 INTO
5 FIELD
5 WHO
5 ARE
5 TWO
5 DIFFERENT
5 CONTRADICTORY
5 WHAT
5 MY
5 ON
5 THEY
4 RESIDUE
4 ABOUT
4 USENET
4 SAME
3 HAS
3 PROVE
3 RATHER
3 FORMULA
3 ALL
3 FROM
3 NUMBERS
3 FOUND
3 SOME
3 CLAIMED
3 SIMPLE
3 BY
3 IDEA
3 NOW
3 KNOW
3 LIKE
3 EQUATION
3 GET
3 THESE
2 PROBABILISTIC
2 ARGUED
2 INTERVAL
2 UP
2 HAD
2 AN
2 BOTH
2 SIDES
2 PROVEN
2 TRUE
2 HOW
2 FACTS
2 USE
2 INTERPRETATION
2 ESTABLISHED
2 WERE
2 OFF
2 UNDERSTAND
2 EASILY
2 PRIOR
2 WAY
2 SIMPLIFICATION
2 WORKS
2 SAY
2 POSTERS
2 ENTERED
2 SEE
2 NO
2 RING
2 ALGEBRAIC
2 INTEGERS
2 NOTICED
2 HAVING
2 ACTUALLY
2 BEEN
2 HUNDRED
2 SELECTED
2 PROB
2 BACK
2 SUCH
2 REALIZED
2 ABLE
2 SOMETHING
2 EVEN
2 FLAW
2 COULD
2 WELL
2 WHERE
2 THOUGH
2 GAP
2 ME
2 CORRECT
2 JUST
2 BECAUSE
2 GOLDBACH
2 CANNOT
2 OPPOSITE
2 PROBABILITY
2 ASSURE
2 BRAINS
2 HOME
2 PURE
2 NORMAL
1 ERUPTED
1 ACTUAL
1 COUNT
1 DIDN
1 OTHERS
1 ALREADY
1 WITHIN
1 OH
1 FORGOT
1 ALSO
1 FIND
1 CONSTANT
1 HTTP
1 MATHWORLD
1 WOLFRAM
1 COM
1 TWINPRIMESCONSTANT
1 HTML
1 CALCULATION
1 UNABLE
1 IGNORE
1 BOLD
1 KEEPS
1 SHIFTING
1 SEEING
1 GO
1 HIGHER
1 LITERATURE
1 DOES
1 GOOD
1 JOB
1 PREDICTING
1 SIMPLER
1 THAN
1 CURRENTLY
1 TAUGHT
1 ARGUE
1 FAIRLY
1 NOTHING
1 FACT
1 CONFIDENTLY
1 PROCLAIM
1 MORE
1 OTHERWISE
1 HUMAN
1 NATURE
1 MIND
1 THERE
1 DOUBT
1 THIS
1 APPROACH
1 TIES
1 NOTED
1 ACTION
1 KNOWN
1 RESEARCH
1 ASSUMING
1 SCARY
1 IMPLICATIONS
1 PUZZLED
1 DISPROVE
1 ONE
1 MAY
1 WORLD
1 ISN
1 EXACTLY
1 BUZZING
1 NEWS
1 YOUR
1 HISTORY
1 STUDY
1 GOT
1 BIG
1 CALL
1 PREFERRED
1 REMARKABLE
1 PUSHED
1 FURTHER
1 MODULO
1 THEN
1 VE
1 EACH
1 SHOULD
1 OTHER
1 TRIVIALLY
1 SHOWN
1 CONTRADICT
1 COMPLEX
1 DO
1 ALLOWS
1 APPEAR
1 WITHOUT
1 GIVES
1 SIMILAR
1 DONE
1 GAPS
1 ARBITRARY
1 NICE
1 SIZE
1 LITTLE
1 TOLERANT
1 DEPRESSING
1 CONVINCE
1 DOESN
1 PROVED
1 TWINS
1 STUCK
1 HEART
1 DISPROVED
1 COURSE
1 SELECTS
1 INSTANCE
1 CAPABLE
1 THEORISTS
1 PERSON
1 PECULIAR
1 ABILITY
1 DID
1 WRONG
1 THOROUGHLY
1 MIGHT
1 WEIRD
1 FEELING
1 WOULD
1 PUSH
1 TOPOLOGY
1 OK
1 TURNS
1 OUT
1 MULTIPLE
1 RESULTS
1 AROUND
1 ALWAYS
1 NONE
1 IMPORTANT
1 LOOK
1 LEADS
1 JOURNALS
1 CONSIDER
1 TOOK
1 WHILE
1 FEW
1 THINK
1 BLOG
1 HAVEN
1 POSTED
1 PUT
1 FLAWED
1 VERSIONS
1 WHY
1 WANDERED
1 WIDE
1 RANGE
1 M
1 RIGHT
1 RECENTLY
1 WON
1 MATTER
1 CORE
1 MEANS
1 BROUGHT
1 SUBJECT
1 MOVED
1 GIVEN
1 ANY
1 QUITE
1 ITSELF
1 DAMN
1 INCONVENIENT
1 EH
1 CONUNDRUM
1 AGAIN
1 DOMINATE
1 DOMINATES
1 DECIDED
1 SPECIAL
1 WHOSE
1 MAKE
1 ALLOW
1 PERFECT
1 TYPE
1 COMFORTABLE
1 SENSE
1 FASHIONED
1 CALLED
1 SECURE
1 NOTICE
1 CAME
1 MADE
1 THEMSELVES
1 ARGUMENTS
1 WILL
1 ANYWHERE
1 TRYING
1 EXPLAIN
1 THEIR
1 WORK
1 NATURAL
1 BREATHING
1 SITUATION
1 KIND
1 FASCINATING
1 MANY
1 WAYS
1 GOD
1 ONLY
1 KNOWS
1 BREAK
1 HOLD
1 THEREFORE
1 JAMES
1 HARRIS
Maybe. If the "prime residue axiom" is in fact, an axiom.
> If yes - where is it?
It's trivial.
> If no - what's stopping you?
>
> I am confused.
The twin primes conjecture is just a special case of what is I guess a
prime gap theorem that follows from the prime residue axiom and the
prime gape equation.
So there are an infinity of any even prime gaps greater than 0.
I've had the idea for over 3 1/2 years. If the world can wait, so can
I.
After all, I have the answer. Out of billions of people. What else
is there?
Posters get angry at me thinking I wish to be famous, but haven't they
noticed something remarkably odd, I'm NOT famous by most people's view
of what that is?
Fame sucks dude. I've escaped it for years just by getting some
people to think I wanted it, and isn't that scary odd? How easy that
was? How to hurt me they gave me what I wanted?
I've debated and debated and debated. Does it really matter to the
freaking world whether or not I'm famous? Why can't I just keep
things like they are now?
Does Peter Pan really have to grow up? Why? Why can't I stay in my
little bubble for decades?
Will it really hurt the world? You have the math. You don't need me.
James Harris
Amen brother - amen!
http://www.crank.net/harris.html
Crank, super-troll, snake-oil salesman, liar and cheat are the terms I
would use to describe you.
You need serious help for your NPD.
Maybe. I don't know. Years ago it was just this notion that I'd find
a simple proof of Fermat's Last Theorem, hoping maybe there was one,
when I believed Andrew Wiles had a proof.
But I mean, how could I REALLY take that seriously? I kind of did but
also it wasn't like there was much of a downside. Try. Fail. So
what?
But the math people on newsgroups went freaking crazy mad insane
vicious.
I will never forget the poster who replied that I was subhuman, why?
He said because I even DARED to consider looking for a simpler proof
of FLT after Wiles.
So part of it early on was just saying, these people will not insult
me into silence.
And they DID insult so many people into silence. Usenet was a zone
where posters BRAGGED about insulting people off of newsgroups.
BRAGGED about it in posts.
Have I really deep down believed that I have these important
mathematical proofs?
I think the real answer is, does it matter? Has it? Mostly it's
arguing on Usenet and having some blogs and things.
And there is that fascinating with math people who seem so obsessed
with ordering people like me around. What's wrong with them? I read
posts by people who try to say anything nasty they can imagine, and
I'm like, why? Why bother? What are they thinking?
There are some things that have happened for sure. One I can't stand
mathematicians. I've learned a real dislike of mathematicians as a
group from years of nastiness on Usenet. There is really, really
something wrong with them as a group I believe. Sad to say, but I
have never seen nastier more vicious people in my life.
And they take themselves so freaking seriously!!!
Dudes. There is more to life than math. None of you are nearly as
important as you think you are.
And you nasty censorship bastards will never be anything really, as
long as you cannot learn to respect the rights of others.
Yeah, sure, you can insult people into shutting up about your pet
bullshit math, but why?
Why?
Does it occur to any of you turds that maybe if you're a monster then
it doesn't matter anyway?
You're still a monster.
James Harris
What do you think it means for something to be an axiom?
You mean like when you wrote the following.
James Harris <jst...@msn.com> wrote:
>If you fucking morons think that I will let you get away with not
>giving me credit for my fucking math discoveries then you have another
>fucking thing coming.
>What the fuck??!!!
>Where's "pure math" now, huh? Where's loving math for the fucking
>beauty of it now you fucking shits??!!!
>LOOK AT IT!!!
>Here is the partial difference equation and instructions for
>integrating.
>dS(x,y) = [p(x/y, y-1) - p(y-1, sqrt(y-1))][ p(y, sqrt(y)) - p(y-1,
>sqrt(y-1))],
>S(x,1) = 0.
>And p(x, y) = floor(x) - S(x, y) - 1, and you get S as the sum of dS
>from dS(x,2) to dS(x,y).
>http://mathforprofit.blogspot.com/
>You fucking shits. I will get credit for my discovery and get fucking
>paid, and you best believe that I will not fucking let you stupid
>fucks get away with your fucking stupid bullshit--"pure math" my
>ass--without me coming at you fuckers with some fucking PURE fucking
>PURE AS FUCK math that you stupid shits have been shitting on for over
>a fucking YEAR!!!
>You goddamn FUCKS!!!
>What the fuck is wrong with you shits??!!! Don't you even believe in
>your own stupid shit? Where's "pure math" now?
>Where is it?
>James Harris
That sounds very interesting. Could you please give me the precise
statement this the "prime residue axiom"?
And could you please show me how how the Twin Prime Conjecture follows
from this "prime residue axiom"?
>
> > If yes - where is it?
>
> It's trivial.
>
Maybe to you. But I may be not as sharp on the Twin Prime Conjecture
as you. So, could you please show me this proof, even if it is
trivial?
>
> > If no - what's stopping you?
>
> > I am confused.
>
> The twin primes conjecture is just a special case of what is I guess a
> prime gap theorem that follows from the prime residue axiom and the
> prime gape equation.
>
> So there are an infinity of any even prime gaps greater than 0.
>
> I've had the idea for over 3 1/2 years. If the world can wait, so can
> I.
>
Well, I am confused now. Do you have a proof of the Twin Prime
Conjecture to share with me right now or not? I am confused.
>
> After all, I have the answer. Out of billions of people. What else
> is there?
>
Do you mean that you have a proof of the Twin Prime Conjecture? If so
- please share with me.
>
> Posters get angry at me thinking I wish to be famous, but haven't they
> noticed something remarkably odd, I'm NOT famous by most people's view
> of what that is?
>
Well, if you have shared with these people your precise proof of the
Twin Prime Conjecture - then these people are very wrong and stupid.
On the other hand, if you haven't given any proofs - then I can see
how your readers would become confused and impatient.
But I need to see your proof first.
>
> Fame sucks dude. I've escaped it for years just by getting some
> people to think I wanted it, and isn't that scary odd? How easy that
> was? How to hurt me they gave me what I wanted?
>
> I've debated and debated and debated. Does it really matter to the
> freaking world whether or not I'm famous? Why can't I just keep
> things like they are now?
>
> Does Peter Pan really have to grow up? Why? Why can't I stay in my
> little bubble for decades?
>
> Will it really hurt the world? You have the math. You don't need me.
>
Well, if you have a proof of the Twin Prime Conjecture, I for one
would love to see it. I would even nominate you for the Abel Prize.
But let me see your proofs.
************************************************************
NPD detection, over 5% indicates serious NPD
18+2+1 =21
21/192 = 10.93%
JSH => you are now at 11% and you are going to POP!
Unique words:192 Total words:391
Freq. Word
18 I
11 OF
10 A
9 IT
9 PEOPLE
9 YOU
7 AND
7 THAT
6 TO
6 THERE
6 AS
6 WAS
5 REALLY
5 SO
5 BUT
5 WHY
4 MATH
4 T
4 THEY
4 HAVE
4 IS
4 WITH
4 ARE
4 ON
4 THE
3 INSULT
3 INTO
3 S
3 LIKE
3 USENET
3 ABOUT
3 PROOF
3 WILL
3 NEVER
3 CAN
3 WHO
3 WHAT
3 MAYBE
2 THESE
2 YEARS
2 ME
2 JUST
2 SILENCE
2 TAKE
2 SERIOUSLY
2 NEWSGROUPS
2 BRAGGED
2 FREAKING
2 IN
2 POSTS
2 VICIOUS
2 IMPORTANT
2 THINK
2 REAL
2 DID
2 DOES
2 MATTER
2 SOME
2 THINGS
2 ONE
2 WRONG
2 THEM
2 SAY
2 ANYTHING
2 NASTY
2 TRY
2 BELIEVED
2 SURE
2 MATHEMATICIANS
2 WILES
2 GROUP
2 MORE
2 LIFE
2 FOR
2 RE
2 MONSTER
1 FERMAT
1 SIMPLER
1 FLT
1 AFTER
1 PART
1 EARLY
1 SAYING
1 KIND
1 NOT
1 NOTION
1 ALSO
1 WASN
1 LAST
1 MUCH
1 DOWNSIDE
1 MANY
1 THEOREM
1 ZONE
1 WHERE
1 POSTERS
1 FAIL
1 HOPING
1 INSULTING
1 OFF
1 KNOW
1 D
1 WHEN
1 DEEP
1 DOWN
1 FIND
1 MATHEMATICAL
1 PROOFS
1 ANDREW
1 DON
1 ANSWER
1 WENT
1 HAD
1 CRAZY
1 HAS
1 MOSTLY
1 ARGUING
1 HAVING
1 MAD
1 BLOGS
1 INSANE
1 FASCINATING
1 SIMPLE
1 SEEM
1 OBSESSED
1 ORDERING
1 AROUND
1 MEAN
1 HOW
1 READ
1 BY
1 FORGET
1 POSTER
1 COULD
1 REPLIED
1 IMAGINE
1 M
1 BOTHER
1 SUBHUMAN
1 THINKING
1 HAPPENED
1 AGO
1 STAND
1 HE
1 VE
1 LEARNED
1 DISLIKE
1 SAID
1 BECAUSE
1 FROM
1 NASTINESS
1 SOMETHING
1 BELIEVE
1 SAD
1 SEEN
1 NASTIER
1 EVEN
1 MY
1 DARED
1 THEMSELVES
1 DUDES
1 THAN
1 NONE
1 THIS
1 NEARLY
1 CENSORSHIP
1 BASTARDS
1 BE
1 LONG
1 CANNOT
1 LEARN
1 RESPECT
1 RIGHTS
1 OTHERS
1 YEAH
1 SHUTTING
1 UP
1 YOUR
1 PET
1 BULLSHIT
1 OCCUR
1 ANY
1 TURDS
1 IF
1 CONSIDER
1 LOOKING
1 THEN
1 DOESN
1 ANYWAY
1 STILL
1 JAMES
1 HARRIS
Well I like mine:
Given differing primes p_1 and p_2, where p1 > p2, there is no
preference for any particular residue of p_2 for p_1 mod p_2 over any
other.
Of course I could fiddle with it. It's like when I defined the object
ring. Took me a while to get it right. Which is so much fun.
> And could you please show me how how the Twin Prime Conjecture follows
> from this "prime residue axiom"?
Oh, that's easy. Consider that if x is a prime number then all that
is required for a twin prime situation is that x+2 NOT equal 0 mod p
for any prime less than sqrt(x).
So assume there is a largest set of twin primes, then it follows that
it never again occurs that the residues avoid that value and in fact
forces that for every case of x a prime out to infinity, there must
always be a case where x+2 = 0 mod p, for some prime less than
sqrt(x), which is a prime preference by residue in contradiction with
the axiom. That is, p will PREFER -2 as a residue mod x, which
contradicts.
Therefore, the twin primes conjecture follows from the "prime residue
axiom". If it is indeed an axiom then it is the twin primes proof.
Notice that key here is just re-thinking what a twin prime is: it is
merely a residue situation where all residues mod p where p is a prime
less than sqrt(x), when x is prime do not have a certain value.
That's all. Nothing more.
Then no prime preference means that situation will keep occurring out
to infinity.
James Harris
Could you please define what you mean by "preference"? In fact, the
term "preference for any particular residue" is totally unclear to me.
I am sure you have a very concrete meaning in mind, but I need a
precise explanation in order to understand what exactly you mean.
>
> Of course I could fiddle with it. It's like when I defined the object
> ring. Took me a while to get it right. Which is so much fun.
>
What is this "object ring" and how do you define it?
>
> > And could you please show me how how the Twin Prime Conjecture follows
> > from this "prime residue axiom"?
>
> Oh, that's easy. Consider that if x is a prime number then all that
> is required for a twin prime situation is that x+2 NOT equal 0 mod p
> for any prime less than sqrt(x).
>
> So assume there is a largest set of twin primes, then it follows that
> it never again occurs that the residues
>
The residues of what with respect to what?
>
> avoid that value
>
Which value?
>
> and in fact
> forces that for every case of x a prime out to infinity, there must
> always be a case where x+2 = 0 mod p, for some prime less than
> sqrt(x),
>
To what do you refer as "some prime" in the above sentence? To x? To
p? Or some other unmentioned variable?
>
> which is a prime preference by residue in contradiction with
> the axiom. That is, p will PREFER -2 as a residue mod x, which
> contradicts.
>
I thought you were talking mod p.
I am confused. Your text seems very promising, but at the moment, I
can't make heads from tails in it. Could you please make your proof/
explanation more precise?
Maybe the problem here is that your proof is very subtle for the minds
of average mathematicians, and they and I need you to condescend to a
more detailed and precise explanation of your proof?
>
> Therefore, the twin primes conjecture follows from the "prime residue
> axiom". If it is indeed an axiom then it is the twin primes proof.
>
> Notice that key here is just re-thinking what a twin prime is: it is
> merely a residue situation where all residues mod p where p is a prime
> less than sqrt(x), when x is prime do not have a certain value.
> That's all. Nothing more.
>
That sounds very enticing and promising. I am sure that when you
explain your proof, to me, I will understand it and support it. But I
need to understand it first.
The object ring is a discovery of mine from years ago.
The object ring is defined by two conditions, and includes all numbers
such that these conditions are true:
1. 1 and -1 are the only rationals that are units in the ring.
2. Given a member m of the ring there must exist a non-zero member n
such that mn is an integer, and if mn is not a factor of m, then n
cannot be a unit in the ring.
No. Consider 29 and 31, twin primes. If you look at primes less than
sqrt(29) you have 2, 3 and 5, where 2 is of course irrelevant as it
always has the same residue modulo an odd.
Notice that 29+2 = 31, 31 mod 5 = 1, and 31 mod 3 = 1. But notice
that 31 + 2 = 33, 33 = 0 mod 3, and 33 is of course not prime.
If prime residues occur without a particular residue favored i.e.
occurring more frequently, then there will always be cases where NONE
of the primes p less than sqrt(x), when x is prime will have a residue
of x+2 = 0 mod p.
What's interesting about this approach to the twin primes conjecture
is that it says the conjecture is NOT about anything other than the
primes which can stop a twin primes situation.
So, for instance, 31 and 33 don't work because 33 is divisible by 3.
3 has no preference for 1 or 2 modulo itself, so 31 mod 3 = 1 is ok,
but 29 mod 3 = 2 is ok as well.
But only 3 and 5 decide. They are the decision primes.
But let's say 3 LIKED 1 as a residue, and preferred it, then how would
that affect the occurrence of twin primes? There'd be fewer.
In the extreme if 3 could force ALL primes to have a residue of 1
modulo itself then there would be no twin primes at all.
James Harris
What do you mean by "units in the ring"?
>
> 2. Given a member m of the ring there must exist a non-zero member n
> such that mn is an integer, and if mn is not a factor of m, then n
> cannot be a unit in the ring.
>
> > > > And could you please show me how how the Twin Prime Conjecture follows
> > > > from this "prime residue axiom"?
>
> > > Oh, that's easy. Consider that if x is a prime number then all that
> > > is required for a twin prime situation is that x+2 NOT equal 0 mod p
> > > for any prime less than sqrt(x).
>
> > > So assume there is a largest set of twin primes, then it follows that
> > > it never again occurs that the residues
>
> > The residues of what with respect to what?
>
You forgot to answer my question.
>
> > > avoid that value
>
> > Which value?
>
You forgot to answer my question.
>
> > > and in fact
> > > forces that for every case of x a prime out to infinity, there must
> > > always be a case where x+2 = 0 mod p, for some prime less than
> > > sqrt(x),
>
> > To what do you refer as "some prime" in the above sentence? To x? To
> > p? Or some other unmentioned variable?
>
You forgot to answer my question.
>
> > > which is a prime preference by residue in contradiction with
> > > the axiom. That is, p will PREFER -2 as a residue mod x, which
> > > contradicts.
>
> > I thought you were talking mod p.
>
> > I am confused. Your text seems very promising, but at the moment, I
> > can't make heads from tails in it. Could you please make your proof/
> > explanation more precise?
You forgot to answer my question.
> > Maybe the problem here is that your proof is very subtle for the minds
> > of average mathematicians, and they and I need you to condescend to a
> > more detailed and precise explanation of your proof?
>
> No.
>
"No" to what question?
>
> Consider 29 and 31, twin primes. If you look at primes less than
> sqrt(29) you have 2, 3 and 5, where 2 is of course irrelevant as it
> always has the same residue modulo an odd.
>
> Notice that 29+2 = 31, 31 mod 5 = 1, and 31 mod 3 = 1. But notice
> that 31 + 2 = 33, 33 = 0 mod 3, and 33 is of course not prime.
>
> If prime residues occur without a particular residue favored i.e.
> occurring more frequently, then there will always be cases where NONE
> of the primes p less than sqrt(x), when x is prime will have a residue
> of x+2 = 0 mod p.
>
> What's interesting about this approach to the twin primes conjecture
> is that it says the conjecture is NOT about anything other than the
> primes which can stop a twin primes situation.
>
> So, for instance, 31 and 33 don't work because 33 is divisible by 3.
> 3 has no preference for 1 or 2 modulo itself, so 31 mod 3 = 1 is ok,
> but 29 mod 3 = 2 is ok as well.
>
> But only 3 and 5 decide. They are the decision primes.
>
> But let's say 3 LIKED 1 as a residue, and preferred it, then how would
> that affect the occurrence of twin primes? There'd be fewer.
>
> In the extreme if 3 could force ALL primes to have a residue of 1
> modulo itself then there would be no twin primes at all.
>
> James Harris
>
James. I don't understand your proof. I asked you specific questions
to clarify your proof, but you didn't answer them. I am trying to
understand your proof, but you are no longer helping me. Could you
please give your proof in a way that is clear to me? In particular,
please answer my questions above.
Thank you.
James, I appreciate that you are trying to give explanations that are
non-technical and can be understood by readers who aren't experts but
sometimes your literary style makes your text very difficult to read.
It's quite possible that the problem lies in the difference between USA
grammar and UK grammar so the following points may not be valid over
there. However, as examples,
.. you know that study ..
I feel uncomfortable without an article on front of study so that it
would be *the* study, or *a* study, or *your* study. I wouldn't write 'I
know that scent of roses is sweet' but perhaps you would.
.. something something, where something ..
You are very fond of this type of text construction and your proofs
sometimes have compound versions to produce the equivalent of 'the scent
of roses is sweet, where sweet is used in the olfactory and not
behavioural sense, where roses are plants and not chocolates'. The
simple version is hard to read and the compound version is even harder
because it looks as if the second qualifier applies to the first
qualifier and not the main sentence. Using a different conjunction might
make the text easier to read and understand.
.. I've proven that ..
Proven is an adjective, not a verb.
.. to contradict with ..
My grand-daughters may contradict me, but they don't contradict with me
unless we are both contradicting someone else. I'd be interested if you
were to say that this is correct usage in the USA because it's something
that has caught me out before. I read a sentence along the lines of "Dr
Mudd's wife met with her husband in The Arsenal" and immediately
wondered whom they met. It took me a while to realise that she met him
(in UK grammar).
Sometimes I'm trying for a literary effect that can be muddled even
for me, as I'm often in experimental mode on the newsgroups.
I will usually try things out here first and then write in other areas
including my blogs, so being rough around the edges doesn't concern me
nearly so much with newsgroup posts.
I do appreciate your comments though, especially on my blog posts,
where I'm a lot more concerned about what I see as the final product.
> It's quite possible that the problem lies in the difference between USA
> grammar and UK grammar so the following points may not be valid over
> there. However, as examples,
>
> .. you know that study ..
>
> I feel uncomfortable without an article on front of study so that it
> would be *the* study, or *a* study, or *your* study. I wouldn't write 'I
> know that scent of roses is sweet' but perhaps you would.
I think that is a US versus UK usage thing, but on the other hand, I
do shift more towards UK usage deliberately at times as proportionally
most of my readers are in the UK!
That is, by number the US and UK are roughly equal by readership, but
then, the US is bigger than the UK, so....
Oh, and also London is my biggest city of readers by far, so I have
reason to try and make my writing more palatable to the English, but
then again, I also see people in the UK as pickier with what you call
the Queen's English, n'est-ce pas?
In this case I was pushing for a higher degree of greater informality!
The study of twin primes is rather huge in mathematics, so I was
deliberately pushing to more of an almost street language for effect.
> .. something something, where something ..
>
> You are very fond of this type of text construction and your proofs
> sometimes have compound versions to produce the equivalent of 'the scent
> of roses is sweet, where sweet is used in the olfactory and not
> behavioural sense, where roses are plants and not chocolates'. The
> simple version is hard to read and the compound version is even harder
> because it looks as if the second qualifier applies to the first
> qualifier and not the main sentence. Using a different conjunction might
> make the text easier to read and understand.
Yeah, I'm bad with compound sentences as I have a conceit of making
very long sentences at times which can be awkward, so I am aware, and
do try to compensate at times, but it's a habit.
I can just so love those long, wordy sentences with so many compounds
in them, but then again, that can be a problem for communication which
is, of course, the big picture point.
> .. I've proven that ..
>
> Proven is an adjective, not a verb.
>
> .. to contradict with ..
>
> My grand-daughters may contradict me, but they don't contradict with me
> unless we are both contradicting someone else. I'd be interested if you
> were to say that this is correct usage in the USA because it's something
> that has caught me out before. I read a sentence along the lines of "Dr
> Mudd's wife met with her husband in The Arsenal" and immediately
> wondered whom they met. It took me a while to realise that she met him
> (in UK grammar).
Here it may be awkwardness of the subject. It IS an odd thing to even
conjecture the ring of algebraic integers showing one thing, while the
field of complex numbers shows the opposite, and I've struggled with
how to describe that concept.
So I wouldn't say it's necessarily about US usage in this case, as in
my own feeling of awkwardness in describing something remarkably odd.
Thanks again for the comments! I want to emphasize though that the
newsgroup posts are what I call rough-and-ready. I'm doing things
rapidly, sometimes just throwing a lot out there to see what sticks!
And I'm doing a lot of experimenting, and trying out different things
for effect.
I am concerned though about ease of readership across countries, but
it's also such a daunting task. For some reason my math blog country
numbers are down, but in the last 30 days I've had hits according to
Google Analytics from people in 461 cities, in 46 "countries/
territories" as Google puts it.
Don't know why the country count is trending down, but also don't know
if it matters. That number covers all the major English speaking
countries--the US, Canada, Australia, UK--and most of Europe and many
other countries as well.
So I don't know if it matters to trend from 50+ countries every 30
days down to just below, but maybe I'm a little disappointed because I
assumed the prime residue concept would trend things up, not down, but
I digress.
James Harris
Idiot.
"No" to what question?
Thank you.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
JSH could not google up a cut and paste answer for them.
JSH is Troll
Maybe "harry" would like to do a word count on that text also.
---
J K Haugland
http://www.neutreeko.net
Meaning that you use this site--a site where many, like myself, come to learn -- as your personal drawing board, to dump your garbage.
And then you want to be treated respectfully in return
>
> I will usually try things out here first and then
> write in other areas
> including my blogs, so being rough around the edges
> doesn't concern me
> nearly so much with newsgroup posts.
What if I were to conduct experiments in _your_ blog.
just like you conduct yours in here.?.What that be O.K with you?
>
>>
> That is, by number the US and UK are roughly equal by
> readership, but
> then, the US is bigger than the UK, so....
All made up by you, until you back this up.
>
> > ..>
>>
> James Harris
Go do your experiments in _your_ blog.
>