## Twin Prime Proof Proffered 179

Posted
by
samzenpus

from the is-this-going-to-be-on-the-test dept.

from the is-this-going-to-be-on-the-test dept.

HateBreeder writes

*"Continuing on a previous slashdot story regarding Arenstorf's proof of the existence of Infinitely Many Prime Twins, it seems that a hole has recently been found in the proof, however mathematicians remain hopeful that the proof can be corrected."*
## Withdrawn (Score:5, Informative)

## Re:Withdrawn (Score:1)

## Re:Withdrawn (Score:5, Informative)

Yeah, it's likely it'll take a long time to fix it.

Gerald Tenenbaum [u-nancy.fr] (the guy who pointed out the mistake) is quite well known, so if he feels that this affects the paper badly, it's probably quite true - and it maybe a while before people get around coming up with an alternative.

(I know this because Tenenbaum is known to my advisor, Jean Bellissard [gatech.edu].)

## Re:Withdrawn (Score:4, Interesting)

(I went to GA Tech for a semester...)

## Re:Withdrawn (Score:5, Informative)

(it might be gone soon, though - it's an arXiv mirror)

Lemma 8 is on Page 35 -

Lemma 8 Let r(v) and (v) of class C1(v0,), 0 r(v) v0 = 1/2 N0; and let (v) in C0(v

*defines an integral limit for K as a function of (T) for certain values of T, and gives the boundary and limit conditions*

Although this made sense, the proof is kinda over my head, though.

Btw - which dept were you at GT?

## Re:Withdrawn (Score:2)

## Re:Withdrawn (Score:3, Informative)

He's one of the people responsible for theoretical QC research in GATech -- along with Chapman and a few other folks from GTRI such as John Cortese.

He's also the former editor of the really respected Theoretical Physics journal, Annales de l'Institut Henri Poincaré.

Brilliant professor, and a wonderful person.

## Re:Withdrawn (Score:2)

I believe Richard Feynman was known to teach first years as well, and he's one of the most important names in physics this century. You think those freshman physics majors in his class were more or less likely to drop out of the program after meeting that guy? Man, I wish I had been college-age when he was still alive and teaching!

## Re:Withdrawn (Score:2, Funny)

## Re:Withdrawn (Score:1, Funny)

## Re:Withdrawn (Score:2)

## I like a good alliteration as much as anyone (Score:5, Informative)

It was proffered a long time ago. The news is that it doesn't work. May I suggest punctured?

## Re:I like a good alliteration as much as anyone (Score:2, Informative)

The act of proffering; an offer.

2. To essay or attempt of one's own accord; to undertake, or propose to undertake

## Re:I like a good alliteration as much as anyone (Score:1, Offtopic)

In any event the coward is correct, proffered is not the proper word to use in this case.

## Re:I like a good alliteration as much as anyone (Score:1, Funny)

Two Prime Proof Poofed

## proffered paired prime proof poofed (Score:2, Funny)

## Re:proffered paired prime proof poofed (Score:5, Funny)

## Re:I like a good alliteration as much as anyone (Score:1)

## Re:I like a good alliteration as much as anyone (Score:4, Interesting)

It was proffered a long time ago. The news is that it doesn't work. May I suggest punctured?A couple years ago, there was a proposed proof to the Poincare conjecture- not the Perelman proof which AFAIK still holds together, but another attempt which was soon found to have an insurmountable problem. When the proof was first announced, the Mathworld news item ran, Poincaré Conjecture Purportedly Proved [wolfram.com], and when the hole in the proof (essentially, an unproven step used in the proof) came to light, the headline was Poincaré Conjecture Purported Proof Perforated [wolfram.com].

## Get MIT on the line, ASAP! (Score:5, Funny)

## Re:Get MIT on the line, ASAP! (Score:5, Funny)

## Re:Get MIT on the line, ASAP! (Score:2)

since when has a maths nerd known where there are infinitely many prime twins!Unfortunately, the proof was only that there _are_ infinitely many of them. Actually finding them is left as an exercise to the reader.

## Re:Get MIT on the line, ASAP! (Score:2)

since when has a maths nerd known where there are infinitely many prime twins!Proffered Prime Twins Proof Porn?

## Re:Get MIT on the line, ASAP! (Score:2, Funny)

## Re:Get MIT on the line, ASAP! (Score:2)

quit watching movies and read a godamn bookReally?

As a matter of fact, I do [metlin.org].

## Re:Get MIT on the line, ASAP! (Score:1)

Btw, it works fine on both Firefox and Mozilla 1.7.3 - do a refresh and it renders fine.

## /. version (Score:5, Funny)

## Hole found in first psots? (Score:1)

Continuing on a previous slashdot story regarding Arenstorf's proof of the existence of Infinitely Many First Posts, it seems that a hole has recently been found in the proof,Are you thinking about the same hole that I am thinking about?

## old news (Score:5, Informative)

## Re:old news (Score:5, Interesting)

When I get more time I want to make a perl script that wgets slashdot.org once an hour and searches google for dupes. It is probably enough to test if any links from present slashdot stories have appeared on the site before, but perhaps I can find a way to pick out relevant title words. Once my script has found a dupe it should pick a few highrated comments from the old thread and repost them :)

## Re:old news (Score:1)

## Develop secure web applications just using Excel (Score:1)

Develop secure web applications just using Excel. [jedox.com]But your site uses PHP... Hmm, does that mean there is no way of making a truly secure web application using only true Micro$oft technologies such as ASP and SQL server?

## Tenenbaum? (Score:2, Funny)

While Arenstorf's approach looks promising, an error in one particular step of the proof (...) has recently been pointed out by (...) TenenbaumDamn him, he claims Linux design is wrong too!

err, does he?

## Re:Tenenbaum? (Score:2, Insightful)

## Re:Tenenbaum? (Score:2)

40% Overrated

10% Informative

Try getting more negative karma from a single post, trolls!

## Re:Tenenbaum? (Score:2)

I never heard anyone shouting t

## Re:Tenenbaum? (Score:2)

Tenenbaum?, posted to Twin Prime Proof Proffered, has been moderated Informative (+1).

Tenenbaum?, posted to Twin Prime Proof Proffered, has been moderated Overrated (-1).

Tenenbaum?, posted to Twin Prime Proof Proffered, has been moderated Funny (+1).

Tenenbaum?, posted to Twin Prime Proof Proffered, has been moderated Overrated (-1).

Tenenbaum?, posted to Twin Prime Proof Proffered, has been moderated Funny (+1).

Tenenbaum?, posted

## Re:Tenenbaum? (Score:2)

## I love.... (Score:5, Funny)

slashdotters aimless wrath,

comments from stupid jerks,

and TWINS!

## Re:I love.... (Score:2, Funny)

Oh wait, that sort says something about us doesn't it.

## Re:I love.... (Score:1)

## Re:I love.... (Score:1, Offtopic)

## Re:I love.... (Score:2)

## Re:I love.... (Score:2)

So, why didn't you double post this?

## twin primes. (Score:4, Interesting)

I always have had an obsession with the pattern of prime numbers. Now and then I get motivated and download a current list of those discovered. With that I try to find some magical pattern, in hopes of finding a secret message or formula explaining reality. When that announcement was made in the previous slashdot story, I did find the claim of infinite primes to be troubling. From my own observations, I believe the gaps between primes may fluctuate greatly but the maximum and minimums grow ever higher. To me these gaps look like some sort of waveform. If I had better coding skills in the manipulation of sound, I would write a program to generate a sound wave out of these numbers. Does anyone know if this has been tried and if so, what was discovered?

## Re:twin primes. (Score:1, Insightful)

aand minima. And I would have thought that the latter tend to grow ever lower...## Re:twin primes. (Score:2)

Now, giben that primes with only one number in between are called twin primes, what about 2 and 3, which are even closer, with nothing in between? Maybe siamese twin primes?

## Re:twin primes. (Score:2)

There exists an uniquely determined pair of siamese twin primes.BTW, there's only one golden mean as well, and it still has a name!

## Re:twin primes. (Score:3, Informative)

it is not a claim, it was proven a long long time ago.

This proof is about infinite number of "prime twins" , primes that are next to each other (like 11-13)

## Re:twin primes. (Score:2)

it is not a claim, it was proven a long long time ago. This proof is about infinite number of "prime twins" , primes that are next to each other (like 11-13)My bad. I meant infinite twin primes, not infinite primes.

## Re:twin primes. (Score:2)

## Re:twin primes. (Score:2)

The product of all primes would be 30. Add 1 to the product, you have 31.

According to the basic "proof" (it's not really a proof, as written) then 31 would be either a new (previously unknown) prime, or a product of primes that are not yet known.

From the "proof":

THEREFORE, it is either a prime number which is not a known prime or a product of primes that are not in the set of all known primesIn my example, 31, we have found a prime number. In

## Re:twin primes. (Score:4, Informative)

## Re:twin primes. (Score:3, Informative)

IMHO, numerology should be treated like any other -ology,Errr, numerology [wikipedia.org] is more of a mystical study, considered to be pseudoscience.

Perhaps you meant Number Theory [wikipedia.org]?

## Re:twin primes. (Score:1)

## Re:twin primes. (Score:2, Informative)

Been up all night, need more sleep.

No. %s/g/sleep/coffee. Better!

## Re:twin primes. (Score:1)

## Re:twin primes. (Score:1)

My karma would take a hit

## Re:twin primes. (Score:2, Interesting)

(n+1)!+2

Of course, this doesn't mean that you have to go all the way to (n+1)! before you can find a run of n numbers without a prime, merely that such a run must exist.

## Re:twin primes. (Score:2)

## Re:Treat any -ology the same? (Score:1)

I guess I overestimated.

## Re:twin primes. (Score:1, Interesting)

There are definitely an infinitely large number of primes. Proof: assume a finite number of primes p1,p2,...,pn (counting from smallest to largest). Then p1*p2*...*pn + 1 is divisible by none of these (hence is prime) and is larger than pn. This is a contradiction of the original assumption, which must therefore be wrong. Hence there are an infinite number of primes.

## Re:twin primes. (Score:3, Informative)

## Re:twin primes. (Score:1)

## Re:twin primes. (Score:2)

## Re:twin primes. (Score:1)

## Re:twin primes. (Score:1)

## Re:twin primes. (Score:2)

## Re:twin primes. (Score:4, Interesting)

Basicly, if you set it up as a probability statement:

p( prime ) -> 0

p( prime pair ) -> 0

The latter will simply go towards 0 a lot faster than the former. All you would need to prove is that there must be one more pair (which is not trivial) and you're done.

Take the greek proof, where you multiply all known primes and add 1. Imagine if you took say, the 1000 smallest primes. All it proves is that there's a prime q <= p1*p2*....*p999*p1000+1. That product will be much much greater than any one of the primes. All it takes it one in the entire interval, and the total is infinite.

Kjella

## Re:twin primes. (Score:2)

First, I assume you mean twin primes. Proving infinite primes is trivial and from ancient Greece. It is a proved fact that there are arbitrarily large gaps in the prime sequence (i.e. infinitely large gaps). And that primes get rarer and rarer, in the limit, infinitely rare. Neither of those means that the number of primes is finite.They are "rare" in some senses, but not others. There are enough of them, for example, that the infinite sum of their reciprocals diverges.

## Re:twin primes. (Score:2)

There are enough of them, for example, that the infinite sum of their reciprocals diverges.Interesting. I'm not challenging the claim, but can you point us to the proof?

## Re:twin primes. (Score:1)

Minor nitpick: q isn't necessarily prime. The smallest counterexample:

2 * 3 * 5 * 7 * 11 * 13 + 1 = 30031 = 59 * 509.

However, it does prove that there are prime numbers larger than the last prime used to construct q, which is sufficient for the purpose of proving there are an infinite number of primes.

## Re:twin primes. (Score:2)

less than orequal to p1*...).(Explanation - the number constructed isn't exactly divisible by any of the primes used to construct it, since it is one more than a multiple of all of them, so either it is prime itself, or it has prime factors which are larger than the "largest prime" used to construct it. So there is no "largest prime".)

## Re:twin primes. (Score:3, Insightful)

It is a proved fact that there are arbitrarily large gaps in the prime sequence (i.e. infinitely large gaps).Yes and no. "Arbitrarily large" is not the same thing as "infinitely large". If there were an infinitely large gap, there couldn't be a subsequent prime.

## Re:twin primes. (Score:1)

To me these gaps look like some sort of waveform. If I had better coding skills in the manipulation of sound, I would write a program to generate a sound wave out of these numbers. Does anyone know if this has been tried and if so, what was discovered?"All your base are belong to us" in a slightly annoyed British accent.

## Re:twin primes. (Score:2)

http://www.amazon.com/exec/obidos/tg/detail/-/006 0 935588/qid=1099578709/sr=8-3/ref=sr_8_xs_ap_i3_xgl 14/103-5861881-0888602 [amazon.com]

Although the title sounds exactly like what you are looking for, it doesn't really talk about music made by primes. Having studied some number theory, I found the math in the book to be fairly basic - but it does give an interesting account of the history of the people involved.

If you are interested in getting a

## Re:twin primes. (Score:1)

For those who find primes fascinating, I can recommend John Derbyshire's "Prime Obsession", a history of the Riemann Hypothesis. The math is kept to alternate chapters so it's reada

## The Real Twin-Prime Proof (Score:3, Informative)

## Re:The Real Twin-Prime Proof (Score:1)

It kind of reminds me of the "proof" that 0 equals 1.

## Re:The Real Twin-Prime Proof (Score:1)

## Re:The Real Twin-Prime Proof (Score:2)

I'm guessing you're probably not the same James Wanless as the tarot reader/whatever?

## Re:The Real Twin-Prime Proof (Score:1)

Wrt your second comment - that is correct - he and I are separate individuals, with no direct connection other than our names - though I do quite like tarot!

## Re:The Real Twin-Prime Proof (Score:2)

(haven't gone through them - yet, merely noticed that there seemed to be a lot of good mathematical content).

You should probably read Primes is in P [iitk.ac.in] - good paper.

PS - There is no such thing as FBT, atleast AFAIK. Is that one of yours? Has it been published/peer reviewed?

## Re:The Real Twin-Prime Proof (Score:1)

Didn't realize for a fact about some of the stuff you have, nice

Almost had me, until I decided to look deeper.

## Re:The Real Twin-Prime Proof (Score:1)

J

## Poor hyperlinking (Score:3, Insightful)

## Serious Error.. (Score:4, Funny)

He forgot to carry the 1

## Way to keep on top of things! (Score:2, Interesting)

## Math humor (Score:4, Funny)

## Please don't start... (Score:5, Funny)

An astronomer, a physicist and a mathematician (it is said) were holidaying in Scotland. Glancing from a train window, they observed a black sheep in the middle of a field.

"How interesting," observed the astronomer, "all scottish sheep are black!"

To which the physicist responded, "No, no! Some Scottish sheep are black!"

The mathematician gazed heavenward in supplication, and then intoned, "In Scotland there exists at least one field, containing at least one sheep, at least one side of which is black."

Upon which the others chorused "Shut up you ****ing pedant!" and hurled him out the train window.

## Re:Please don't start... (Score:3, Funny)

## Well, you know what they say... (Score:1)

Physicists think that reality imitates equations

Mathematicians can't make the connection

## Re:Please don't start... (Score:2)

A few days ago, I ran into an old friend of mine. He's a mathemetician, and taught me a lot about programming when I was learning. We chatted for a few minutes, and as we were parting ways, he called "Have a Merry Christmas!". I told him "You're jumping the gun - tomorrow is Halloween."

He replied "I always get those mixed up, because OCT 31 = DEC 25."

## Re:Math humor (Score:1, Funny)

Let odds be even...

## Re:Math humor (Score:2)

## Correcting 'proof'? (Score:4, Funny)

"however mathematicians remain hopeful that the proof can be corrected."Sounds a lot like Republicans.

## Good thing we are all really nerds here (Score:3, Insightful)

## Re:Not quite ready for prime time (Score:5, Insightful)

## Re:My Twin Prime problems (Score:2)

You really should move to The Twin Cities. Surely that cold clime would solve the twin prime problem...

## She said yes! (Score:2)

http://www.gotSheep.com/EMK

Thanks for the good luck