Twin Prime Proof Proffered

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."

Comments

Withdrawn

[Agret]

The paper has since been withdrawn with the reason "A serious error has been found in the paper, specifically, Lemma 8 is incorrect."

Re:Withdrawn

[metlin]

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

Gerald Tenenbaum (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.)

Re:Withdrawn

[gartogg]

I understand that it's flawed, but Is there any place the original (flawed in lemma 8) proof can be viewed?

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

Re:Withdrawn

[metlin]

Here is the original paper.

(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 ,) be such that

*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?

I like a good alliteration as much as anyone

[Anonymous Coward]

Probably more than most. Sadly, that's not what proffered means.

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

[reverseengineer]

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, 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.

Get MIT on the line, ASAP!

[dabigpaybackski]

Who's that weird janitor kid who keeps doing equations on the hallway chalkboards? Maybe he could help out with this.

Re:Get MIT on the line, ASAP!

[Anonymous Coward]

since when has a maths nerd known where there are infinitely many prime twins!

/. version

[cheezemonkhai]

"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, however mathematicians remain hopeful that the proof can be corrected."

old news

[Anonymous Coward]

The mistake was found back in June

Re:old news

[gnalle]

A simple Google search reveals that the story is a dupe. Search the old threads for cool comments to boost your karma :)

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 :)

I love....

[Ingolfke]

scientists doing math,
slashdotters aimless wrath,
comments from stupid jerks,

and TWINS!

twin primes.

[rubberbando]

Before I go into my spiel, I will admit that I am no scientist or mathematician.

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.

[fymidos]

>claim of infinite primes to be troubling

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.

[isometrick]

I think the average maximum difference between primes may increase as primes grow higher (prime density decreases), but twin primes (primes of form p and p+2) continue to exist so the minimum difference for any range can still be very low. IMHO, numerology should be treated like any other -ology, but I did find one reference to what you are talking about: The Music of the Primes, however the site seems to be gone/down. Good luck with your search!

Re:twin primes.

[Kjella]

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.

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

The Real Twin-Prime Proof

[bearnol]

http://www.bearnol.pwp.blueyonder.co.uk/Math/wanle ss2.html

Re:Not quite ready for prime time

[Anonymous Coward]

Umm.... cryptography? You ever use SSL?

Serious Error..

[D-Cypell]

[i]it seems that a hole has recently been found in the proof[/i]

He forgot to carry the 1

Math humor

[Brian Kendig]

At a conference, a mathematician proves a theorem. Someone in the audience interrupts him: "That proof must be wrong. I have a counterexample to your theorem." The speaker replies, "I don't care, I have another proof for it."

Please don't start...

[Lifewish]

An example of the maths humour genre from my Director of Studies (who was pissed at the time):

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. ...it seemed funnier at the time. Specially after the Zorb's Lemon joke.

Re:proffered paired prime proof poofed

[HMA2000]

Previously Proffered Paired Prime Proof Pwn3d!

Correcting 'proof'?

[Rirath.com]

"however mathematicians remain hopeful that the proof can be corrected."

Sounds a lot like Republicans.

Good thing we are all really nerds here

[Hao Wu]

Luckily since we are all true "geeks" here at Slashdot, we can understand this math as we read through it. It's not like we're all posers who are really only interested in trendy politics, media, and video games.