On the Infinity of Twin Prime and other K-tuples

[jzakiya]

Originally Posted by mathwiz

How can data "empirically establish" the Twin Primes conjecture? With a finite amount of data, you cannot prove the infinitude of twin primes.

You can make claims like "well it sure looks like there will be!" But that's not a proof.

Sigh, here we go again...

Please read my paper (and try to understand it) and/or look at my video on it.

The structure of the data, based on their primorial generating forms, establish all the residue gap values, from 2 to any n, only increase in frequency with increasing Pm# generators.
Thus, there is no mathematical possibility for the gaps between primes to ever decrease, let alone ever become zero (0) at some unknown point way up the number line, for any gap size n.
It is structurally impossible for there to be a last prime pair for any gap size n.
As I said, the obvious is so hard to get people to accept. :(

[slandrum]

Originally Posted by jzakiya

... obvious ...

You keep using that word. I do not think it means what you think it does.

[mart_r]

I'm really happy to get a reply, so I've attached the data for p>=43.
Strange... I thought I read the word "Pari" in one of your posts, so I thought you were already using this program.

Originally Posted by jzakiya

As you use more and more consecutive primes for a generator's modulus size Pm#, the number of new consecutive primes from r0 to r0^2 grows, and their gap spacing (and group tuples) grow without end, and will contain every possible gap|tuple combination possible as m -> infinity.

The problem is that you can't easily calculate the first occurrence of a specific tuple, that is, without explicitly checking every number coprime to m# whether or not it's prime. We don't have unconditional proof yet that there's always a prime between n² and (n+1)² for all sufficiently large n. The lack thereof poses a loophole to your theory.

There are also a lot of self-proclaimed proofs for the Riemann Hypothesis (I've even seen one recently on arXiv). Most of them have been confirmed wrong, and the remaining have not been confirmed correct yet.

If it's any consolation, a lot of things seem "obvious" from the numbers, but have been proven wrong. Just take the incompatibility of the first and second Hardy-Littlewood conjectures for instance.

[mart_r]

Originally Posted by jzakiya

As I said, the obvious is so hard to get people to accept. :(

We would like to believe that Polignac's conjecture is correct. All the numbers explicitly calculated so far are in favor of the conjecture, and we have asymptotic formulas that predict the number of occurrences of prime tuples with almost incredible accuracy. You probably won't find anyone who believes the conjecture is wrong.

BUT the only thing we know for sure, backed by stringent mathematical proof, is that there is at least one even number m <= 246 such that infinitely many prime pairs m apart exist. That's all.
Yes, the obvious can be hard to accept. The not so obvious is even harder to accept.

[retina]

Originally Posted by jzakiya

As I said, the obvious is so hard to get people to accept. :(

It doesn't matter how "obvious" it is (or isn't).

Without a proof you have nothing.

So prove it.

[mart_r]

Originally Posted by retina

It doesn't matter how "obvious" it is (or isn't).

Without a proof you have nothing.

So prove it.

Were you addressing jzakiya? With the "not so obvious" I was referring to the lack of proof for Polignac's conjecture. Or so I assume.

[retina]

Originally Posted by mart_r

Were you addressing jzakiya? With the "not so obvious" I was referring to the lack of proof for Polignac's conjecture. Or so I assume.

Yes, I meant to reply to jzakiya. I pressed "Quote" on the wrong post.

[jzakiya]

Originally Posted by retina

It doesn't matter how "obvious" it is (or isn't).

Without a proof you have nothing.

So prove it.

I've been very reluctant to even respond to these type of ad hominem statements,
because they have nothing to do with my work, and are mainly political statements
(in the sense they are devoid of any mathematical content).

Let me guess, you've never read my paper(s), or seen my video. Right?
You have no idea what I've presented as the mathematical basis of my "proof". Right?
If your life depended it on it you couldn't accurately state what I say constitutes my proof. Right?

So do this:
Print out my paper(s), and take out a magic marker, and highlight EXACTLY what you think are
mathematically erroneous, and/or inconsistent, and unproved statements, and why.
Then write down these passages, citing the erroneous content, with page and paragraph number.
Then post here these exact passages from MY WORK you have issues with, and then, and only then,
can we have a genuine discussion about the math that I've presented, and the arguments I make.

But really, I don't think you really care anything about the math I've presented, because you've had
the opportunity (along with everybody else) to already do this, so we could have a mathematical discussion.

Apparently all you have the time to do is make off hand statements about things you have no knowledge of.
And unfortunately, you represent a large portion of the people who've similarly commented in this forum.

If I'm wrong, SHOW ME WHERE IN MY WORK I'M WRONG!!
If YOU (et al) can't do that, then save yourselves some time and just leave it alone.

[Batalov]

Originally Posted by jzakiya

... to even respond to these type of ad hominem statements,
...and are mainly political statements

More word salad!
This is already the second topic beyond math where you use words without understanding their meaning.

Originally Posted by jzakiya

Let me guess, you've never read my paper(s), or seen my video. Right?

Wrong.

Originally Posted by jzakiya

You have no idea what I've presented as the mathematical basis of my "proof". Right?

Wrong.

Originally Posted by jzakiya

If your life depended it on it you couldn't accurately state what I say constitutes my proof. Right?

Wrong.

[mart_r]

Section 6, "The Infinity of Primes": "Thus, any prime p can be treated as r0 to a Pn modulus composed of all the primes < p, whose residues from p to p² are new primes. We can repeat this progression of primes process forever, to always generate new primes."

This last statement is derived from numerical data only. You haven't given proof that we are guaranteed to always see another prime when going from e.g. p² to (p+2)² - while at every such step one prime is taken away at the start of the interval.

Common counterexample: From numerical data only, one might deduce that Li(x)-pi(x) is always positive, but we've known for over a century now that this is not the case for all x. The number of primes between p² and (p+1)² show similar fluctuations, albeit not as large as those Li(x)-pi(x) values. Yet, how can we be sure that this number doesn't drop down to zero at some p?


Section 9, "Proof By Contradiction": "Thus for there to be a finite number of Twins|Cousins, et al, we must have a1 = a2 = 0 starting with some Pn, and remaining so forever."

No, since you're looking at a PGS of finite structure, as opposed to the infinite structure of prime numbers. The problem is eventually related to what I wrote above.


Did I miss something else?

[mathwiz]

If you're right, why haven't you submitted your proof to a reputable mathematics journal?

Also, please learn what "ad hominem" means.