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."

Withdrawn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The paper has since been withdrawn with the reason "A serious error has been found in the paper, specifically, Lemma 8 is incorrect."

I like a good alliteration as much as anyone

[Anonymous Coward]

Probably more than most. Sadly, that's not what proffered [reference.com] 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

[Agret]

To offer for acceptance; tender. See Synonyms at offer.

The act of proffering; an offer.

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

old news

[Anonymous Coward]

The mistake was found back in June [nodak.edu]

Re:Withdrawn

[metlin]

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].)

The Real Twin-Prime Proof

[bearnol]

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

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 [google.com], however the site seems to be gone/down. Good luck with your search!

Re:twin primes.

[metlin]

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.

[metlin]

Ah, my bad. I thought you were talking of Primes in P w.r.t. numerology, and being a physicist completely ignored the rest of the content =)

Been up all night, need more sleep.

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

Re:Withdrawn

[metlin]

Here is the original paper [stanford.edu].

(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?

Re:twin primes.

[miskatonic alumnus]

You cannot conclude that p1*...pn+1 is prime. For example 2*3*5*7*11*13+1 = 30031, which is divisible by 59, hence NOT prime. However, what you CAN conclude is that p1*...pn+1 is either prime, or has a prime factor larger than any of the given pk's.

Re:Withdrawn

[metlin]

Bellissard seriously rocks.

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.