Tuesday, February 11, 2014

Twin-Prime Problem and Goldbach Conjecture Solved?

I was tipped off about this by a reporter at our local newspaper: a local man, James P. Moore, is apparently claiming a solution to the twin-prime problem and the Goldbach conjecture. I haven't read his work. However, the manner in which the claim is being made raises real questions about its correctness.

Moore is apparently not a mathematician by training. Here it is stated that he has a systems design engineering degree from Waterloo.

According to MathSciNet, the database that attempts to review every mathematical publication of interest, Moore has not published any mathematical papers, at least under the names "James P. Moore" or "J. P. Moore". The chances that an amateur without previous mathematical publications could solve these important and famous problems are, for all practical purposes, zero. (Prior to his celebrated recent success on the twin-prime problem, Yitang Zhang, a professional mathematician, had two published papers in good journals.)

Instead of placing his claimed solution on the arxiv, or publishing it in a journal -- as would be customary in such a case -- Moore is selling his solutions online in three different books for $27.05 each. One book is entitled either "The Proof of the Primes" or "The Proof of Primes", a title that doesn't make much sense mathematically.

Moore apparently is working with a public-relations firm to get the news out about his work. You can listen to an interview with him here; it is one of the most painful interviews I have ever heard, largely because the interviewer seems to have no comprehension at all about what the solution might consist of -- she keeps referring inexplicably to DNA -- and seeks to fill the time by repeating the same information over and over.

Moore gave a talk yesterday at the University of Waterloo, but I didn't attend. It wasn't sponsored by the Pure Mathematics department, though. As far as I can see, his public-relations firm hired the room. Again, that's not a good sign.

Here his PR firm suggests that his solution consists of "developing a formula capable of generating every prime number progressively and perfectly". This would not be of much interest, since such formulas are already known. The page also claims that such a method would "create stronger security systems". This is a common misunderstanding; encryption systems such as RSA, while they use prime numbers, would essentially be unaffected by faster ways to generate them. RSA's security would be affected by faster ways to factor products of two or more primes, which is a very different and essentially unrelated problem.

If amateurs think they have solved a famous problem, probably the best route to fame and fortune is to post the paper to a preprint archive. If you can't get an endorser for the arxiv, there's always vixra. Believe me, if your solution is correct, or even close to correct, you'll be acclaimed rather quickly. Hiring public-relations firms and selling your solution in books pretty much guarantees you will be ignored.

Addendum: here Mr. Moore claims, about the primes, that "there is no equation to define them". This is certainly false. They can be defined by a number of different equations; for example, see the talk by my colleague Eric Rowland here.

Another addendum, February 23 2014: Someone showed me a copy of Moore's claimed "proof" of Goldbach's conjecture. Needless to say, it is not correct, and introduces no new ideas at all.


Unknown said...

You will have seen the article at
in which you are extensively quoted.

Unknown said...

Moore doesn't claim on his Facebook page to be a world expert in mathematics, but in "Mathematics DNA" (whatever the F that is).

And I'm a world-class banjo athlete.

Jeffrey Shallit said...

Well, liver, here he apparently claims to be 'one of the world's "leading experts on prime numbers"'.

Unknown said...

I think this commenter (Paul) said it best:

"Perhaps the story should have been titled "Man escapes mental institute" Seriously don't give the idiots ink.Remember the old guy years ago who had harnessed the earths magnetic field for free energy? But nobody believed him ? Put this in the joke section."

I've been a super-big advocate of green energy my entire life. But, this guy really is an embarrassment to green energy advocates (thankfully, not an embarrassment to mathematicians, because he isn't one).

I've done SOME engineering (mostly in college, a little on the job) in my life. Sure, it's hard. But, it did not prepare me for the cold blast of abstraction in higher mathematics in graduate school when I went on to earn a PhD in Math. First semester in grad school: 3 Cs and 1 B. It was a REAL struggle playing catch up, as I was not an undergraduate math major.

This "thinking one can solve some famous math problem" tends to be a sickness more of engineers than anyone with pure abstract math training.

BTW: I originally did not want the name "liver" in my name. Wanted a certain different male body part, as a way of saying FU to the kidnapping & corruption of YouTube by Google+. But, I think their automatic censors (sensors?) wouldn't allow me to use that name.

Ok, I'll stop now.

Takis Konstantopoulos said...

Have you guys seen this "work" by a certain Thierno M. Sow, claiming that he proved the ABC Conjecture, the Beal Conjecture, the Goldbach Conjecture, the Riemann Hypothesis and the Twin Primes Infinity, in a 12-page paper?

jwaltos said...

To me, a mathematician is an imaginative symbolic artist who can fashion aspects of reality. For some it`s a vocation, others a passion. For a few it`s both.

Arthur C. Clarke may have said this, `some people are educated beyond their intelligence.` The converse is true also.

A professional is usually someone who earns their livelihood exercising a skillset. Professionalism is different. The contrast was made clear on many levels in that short article in the entertainment section. I found it amusing, though not out of place, that you would be the voice of reason.
The Amazing Randi should smile.

Unknown said...

As developer of the Unsolved Problems web site at
I can confirm that there are many, many kooks out there. Strangely, despite all being absolutely confident they have solved one or more of the problems, very very few are willing to part with $49, have their article published online, win a prize of $500, and achieve worldwide fame! I wonder why?

Unknown said...

I developed a new prime numbers finding algorithm and by using different mathematical method I aprroved the twin prime numbers conjecture , you can see démonstrations in the file on my blog

Unknown said...

I developped a new prime numbers finding algorithm and by using different mathematical method I approved the twin prime numbers conjecture and GoldBach conjecture , you can see démonstrations on my blog

Jeffrey Shallit said...

No, you didn't.

Unknown said...

did you see my démonstrations?

Jeffrey Shallit said...

Yes. There is nothing resembling a proof in there.

Takis Konstantopoulos said...

If you read his comment above, he doesn't say he proved the twin prime conjecture; he only said

I aprroved the twin prime numbers conjecture.

That is, the conjecture has his approval. If you look at Section 6 of his paper, you will see that it is titled

Mathematical approval and signification of inverse prime number numbers [sic].

Thus, not only does he give his approval, but also his mathematical approval.

Unknown said...

Hi Mr Shallit,
Could you please give me your email adress or writte on my email adress , this is regarding a cooperation in Beal's conjecture.

Jeffrey Shallit said...

Mr. Rhafli: I am not interested in any "cooperation" on Beal's conjecture with you, especially if you cannot manage to figure out my e-mail address through a google search.

e2theipi said...
This comment has been removed by the author.
Unknown said...

Do you see any flows ?

Jeffrey Shallit said...

I don't read stuff on academia.edu. But rest assured if there were a "neat and brief way", it would have been found long ago.

Unknown said...

did you see the paper text I uploaded as to evade Academia in your case ?

Jeffrey Shallit said...

It's completely inappropriate to post a paper to the comments of a blog. Use the arxiv, or vixra, to post your papers.

Unknown said...

I was looking forward to your considerate opinion Mr Shallit

Jeffrey Shallit said...

Without even looking at it I can tell you it's wrong.

Unknown said...

nevertheless take a look at it
Also take look at the following ... primes are not random
The Fundamental Theorem of Arithmetic and proving that the Primes are not Random by Reductio ad Absurdum - By Constantine Adraktas, MIT Alumnus

The Prime Numbers have been tormenting famous Mathematicians since antiquity and all famous Mathematicians consider them to be Random Numbers.

Lectures given by Professors Richard Taylor and Terence Tao and testify to this belief (see their lectures in U Tube under "Primes and Equations | Richard Taylor - Videos from the Institute of Advance Study" and "Terence Tao: Structure and Randomness in the Prime Numbers, UCLA" respectively).

However, using the Fundamental Theorem of the Arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every Integer Number greater than 1 is either a Prime Number itself or is the product of Prime Numbers and that this product is unique, up to the order of the factors.

one concludes that the Prime Numbers, the building blocks of the Composite Numbers, are not Random Numbers.
Set all αi = 1 and keep at least two primes pi
The emerging products combinations are Composite Number, ie not Random Numbers
Hence by Reductio ad Absurdum it is proven that the Primes are not Random, as Order (Composite Numbers) cannot be created by Randomness - Chaos (Prime Numbers)

Constantine Adraktas, MIT
Telephone: 00 - 30 - 6944 - 314 - 309

Jeffrey Shallit said...

You don't understand what it means when a mathematician says "the primes are distributed randomly". It is not a formal statement; it is more an imprecise claim about the distribution of primes. For example, if you look at the primes modulo 4, the primes are roughly equidistributed in the residue classes 1 and 3. There are, of course, limits to this kind of randomness.

It is a completely false claim to say "all famous Mathematicians consider them to be Random Numbers".

Takis Konstantopoulos said...

It's amazing, isn't it, that someone would use phrases like "Prime Numbers, the building blocks of the Composite Numbers, are not Random Numbers" in trying to support an, allegedly, mathematical proof. That's why the world is coming to an end. :-) People don't understand elementary concepts.

Unknown said...

Allow me to refer you to Professor Zagier

In a 1975 lecture, Don Zagier commented

"There are two facts about the distribution of prime numbers of which I hope to convince you so overwhelmingly that they will be permanently engraved in your hearts.

The first fact is that, despite their simple definition and role as the building blocks of the natural numbers, the prime numbers grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout

The second fact is even more astonishing, for it states just the opposite: that the prime numbers exhibit stunning regularity, that there are laws governing their behavior, and that they obey these laws with almost military precision" (Havil 2003, p. 171)

Unknown said...

please see this by Professor
on prime randomness

Jeffrey Shallit said...

So what? Did Don Zagier claim a proof of "the prime numbers are random"? No, he didn't. He was just speaking metaphorically.

Your problem is that you have no understanding of what Zagier was saying.

Jeffrey Shallit said...

No, I have no interest in youtube videos. If you are talking about mathematics, cite results in papers or books, not videos. You're behaving like a crackpot.

Unknown said...

Sorry but it is not a whatever U Tube ... it is a lecture Prof Terence Tao has given in several places ... he knows mathematics ... correct ?

Unknown said...

"I have no interest in youtube videos ... You're behaving like a crackpot". Is Prof Terence Tao a crackpot since he is using U Tube for one of his most famous lectures?
Also Prof Richard Taylor of IAS ? It is an IAS video !

Jeffrey Shallit said...

Go away, you are boring and unwilling to learn.

Unknown said...

Manners and proper language Mr Shalit
And if you and Mr Konstandakatos object to my using the term "random primes" I would like to suggest you mention that in here

and teach a lesson to Professor Tao ... as a Canadian hopefully you have a sense of British humour

Jeffrey Shallit said...

What part of "go away" don't you understand?

I'm not Canadian.

You still don't understand anything about randomness or what is meant by the primes behaving randomly.

Takis Konstantopoulos said...

Mr Adraktas, should I suppose that by "Mr Konstandakatos" you refer to me? If so, you got my name wrong. I tried to look at your paper. But that site is the most annoying site I've ever seen. It started asking my identity, my occupation, it asked me to upload a paper, etc. I'm not interested in proving to the site who I am before taking a look at your paper. The very fact that your paper is uploaded on a commercial site fishing for data makes it fishy. Anyway, I insisted and downloaded your paper and as soon as I saw it I exclaimed "holy shit!" OK, this is its content. I reproduce it here in its entirety:

Goldbach's conjecture proven and in a neat and brief way by Constantine Adraktas

Every even integer greater than 2 can be expressed as the sum of two Primes

All the Prime numbers (bar 2 and 3) reside in the [ 6α + 5 ] and [ 6α + 7 ] vectors

[ 6α + 5 ] = [ 6α + 6 ] - [ 1 ] and [ 6α + 7 ] = [ 6α + 6 ] + [ 1 ]

There are 3 possible sums ( Σ ) combinations involving these vectors

Σ of each element of [ 6α + 5 ] with each element of [ 6α + 5 ] producing the [ 6α + 4 ]
vector bar the number 4

Σ of each element of [ 6α + 5 ] with each element of [ 6α + 7 ] producing the [ 6α + 6 ]
vector bar the number 6

Σ of each element of [ 6α + 7 ] with each element of [ 6α + 7 ] producing the [ 6α + 8 ]
vector bar the number 8

The [ 6α + 4 ] - [ 6α + 6 ] - [ 6α + 8 ] vectors cover all the even integers hence the 3 sums

above cover all the even integers (bar 4 - 6 - 8 which are the sums of 2 + 2 - 3 + 3 - 3 + 5
that is the sums of Primes)

QED .... Goldbach's conjecture proven and in a neat and brief way

I think that what Jeff Shallit is trying to tell you is that there is no chance in a trillion that what you wrote can be considered a mathematical proof of a theorem. To make an analogy, what he's saying is that you behave like someone who listened to great pianists perform Rachmaninoff's Piano Concertos who, one day, decided to play it himself too without ever having played anything on the piano before. Something like that. Or it's like me going to Olympic Games and pretending I got the gold medal in weight lifting. I can't do it.

Unknown said...

Professor Shallit
Would you please take a look at a very short paper (2 pages) by Matilda Walter -
On finding all solutions to the Goldbach problem for 2N - vixra.org 1607.0359
The paper does not claim a proof of G.C.,in fact it explicitly disclaims it. It presents an algorithm finding all solutions for a given even number.


Jeffrey Shallit said...

It's completely trivial to find all solutions for a given number. And it cannot be done efficiently (in log N) because the output size in bits is almost certainly something like N. So it has no interest for anyone.

Unknown said...

Professor Shallit
The algorithm presented in the paper sieves through primes less than or equal to N, where 2N is the number in question. I do not see how this could possibly be done in logN
since you do have to look at all these primes as potential solutions.

Unknown said...

Professor Shallit

I won't bother you anymore. The output is proportional to N/logN the approximate # of primes less than or equal to N, for even #2N

Jeffrey Shallit said...

I was talking about output size in bits, not number of solutions.

Ken Abbott said...

Forget proofs of the Goldbach and Twin Primes Conjectures. But here is a very nice connection between them. It's a way stronger version of the Goldbach Conjecture.. http://www.math-math.com/2018/01/goldbach-conjecture-meets-twin-prime.html

Unknown said...

I do not get it ... please elaborate further

Jeffrey Shallit said...

Ken, that's not original with you. See http://oeis.org/A007534