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Twin Prime Proof Proffered

Posted by samzenpus on 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."

39 of 179 comments (clear)

  1. Withdrawn by Agret · · Score: 5, Informative

    The paper has since been withdrawn with the reason "A serious error has been found in the paper, specifically, Lemma 8 is incorrect."

    --
    Have you metaroderated recently?
    1. Re:Withdrawn by metlin · · Score: 4, Informative


      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.)

    2. Re:Withdrawn by gartogg · · Score: 3, Interesting

      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...)

      --
      I'm a concientious .sig objector.
    3. Re:Withdrawn by metlin · · Score: 4, Informative

      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?

    4. Re:Withdrawn by metlin · · Score: 2, Informative

      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.

    5. Re:Withdrawn by TheOtherChimeraTwin · · Score: 2, Funny

      Before they patch the problem, what are the chances that someone will develop an exploit? And will that let them root the system?

  2. I like a good alliteration as much as anyone by Anonymous Coward · · Score: 5, Informative

    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?

    1. Re:I like a good alliteration as much as anyone by Agret · · Score: 2, Informative

      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

      --
      Have you metaroderated recently?
    2. Re:I like a good alliteration as much as anyone by reverseengineer · · 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, 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.

      --
      "FDA staff reviewers expressed concern about the number of patients who were left out of the study because they died."
  3. Get MIT on the line, ASAP! by dabigpaybackski · · Score: 5, Funny
    Who's that weird janitor kid who keeps doing equations on the hallway chalkboards? Maybe he could help out with this.

    --
    "OH SHIT, THERE'S A HORSE IN THE HOSPITAL!"
    1. Re:Get MIT on the line, ASAP! by Anonymous Coward · · Score: 2, Funny

      Yeah, this is actually the one time that Matt Damon is ON TOPIC...

    2. Re:Get MIT on the line, ASAP! by Anonymous Coward · · Score: 5, Funny

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

  4. /. version by cheezemonkhai · · Score: 5, Funny

    "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."

  5. old news by Anonymous Coward · · Score: 5, Informative

    The mistake was found back in June

    1. Re:old news by gnalle · · Score: 5, Interesting
      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 :)

  6. Tenenbaum? by Vo0k · · Score: 2, Funny

    While Arenstorf's approach looks promising, an error in one particular step of the proof (...) has recently been pointed out by (...) Tenenbaum

    Damn him, he claims Linux design is wrong too!

    err, does he?

    --
    Anagram("United States of America") == "Dine out, taste a Mac, fries"
    1. Re:Tenenbaum? by nbert · · Score: 2, Insightful

      G. Tenenbaum != Andrew S. Tanenbaum

      --
      I don't read replies by ACs.
  7. I love.... by Ingolfke · · Score: 5, Funny

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

    and TWINS!

  8. twin primes. by rubberbando · · Score: 4, Interesting

    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?

    --
    DEAD DEAD DEAD DELETE ME
    1. Re:twin primes. by fymidos · · Score: 3, Informative

      >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)

      --
      Washington bullets will simply be known as the "Bulle
    2. Re:twin primes. by isometrick · · Score: 4, Informative

      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!

    3. Re:twin primes. by metlin · · Score: 2, Informative

      IMHO, numerology should be treated like any other -ology,

      Errr, numerology is more of a mystical study, considered to be pseudoscience.

      Perhaps you meant Number Theory?

    4. Re:twin primes. by metlin · · Score: 2, Informative

      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!

    5. Re:twin primes. by Kjella · · Score: 4, Interesting

      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

      --
      Live today, because you never know what tomorrow brings
    6. Re:twin primes. by locofungus · · Score: 2, Interesting

      It's trivial to prove that there is an arbitrarily long sequence of numbers with no primes in it.

      (n+1)!+2 ... (n+1)!+n+1 is a run of n numbers none of which are prime.

      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.

      --
      God said, "div D = rho, div B = 0, curl E = -@B/@t, curl H = J + @D/@t," and there was light.
    7. Re:twin primes. by miskatonic+alumnus · · Score: 2, Informative

      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.

    8. Re:twin primes. by Rufus88 · · Score: 2, 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.

  9. The Real Twin-Prime Proof by bearnol · · Score: 3, Informative

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

  10. Re:Not quite ready for prime time by Anonymous Coward · · Score: 5, Insightful

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

  11. Poor hyperlinking by BarryNorton · · Score: 2, Insightful

    While Slashdot stories (unlike most of the Flash-based web) can be a good example of hyperlinking, this story (after the first link) was appalling - why was the link to the withdrawal placed around the words 'infinitiely many twin primes'? Not only did I immediately wonder why there seemed to be no link to evidence of the withdrawal, but there was no direct link to explain what the twin prime conjecture is...

  12. Serious Error.. by D-Cypell · · Score: 3, Funny

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

    He forgot to carry the 1

  13. Way to keep on top of things! by HiLander4237 · · Score: 2, Interesting

    News that's only 5 months out-of-date.

  14. Math humor by Brian+Kendig · · Score: 3, Funny

    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."

  15. Please don't start... by Lifewish · · Score: 5, Funny

    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.

    --
    For the love of God, please learn to spell "ridiculous"!!!
    1. Re:Please don't start... by RichDice · · Score: 2, Funny
      Here's the joke that completely killed me and my friends doing physics & astronomy degress back just a tad more than a decade ago...

      There once was a very wealthy man who enjoyed greatly betting on horse races. As he was motivated to win in all his endeavours, he desired to find a perfect method for placing his bets at the track.

      To this end, he hired three experts whom he set upon the task of finding a perfect betting system. They were a biologist, a statistician, and a physicist. He gave them a year to investigate and told them to present their results after the year was up.

      When it was time to present the results, he gathered them together.

      "Did you find a perfect system?" he asked the biologist. "I studied everything I could about the muscular power, reflex reaction time, diet, training, and many other things. Unfortunately the variables were just too complicated and there were too many of them, so I couldn't find a perfect system."

      Not a problem, thought the man, I have two other experts. So he asked the statistician if he had found a perfect system.

      "I analyzed every piece of data that I could: track condition, weather conditions, time of day, jockey, competitors, age of the horse... just everything. I ran every regression I could. But there were just too many variables and I couldn't develop a predicable model from them."

      Now the man was concerned, so with hestitation he asked the physicist if he had discovered a perfect system for betting on horses at the race.

      "Yes!" exclaimed the physicist, "I have!"

      "Terrific!" said the man.

      "Well," started the physicist slowly, "there is one problem. It only works for spherical horses moving through a vacuum."

      Cheers,
      Richard

  16. proffered paired prime proof poofed by dominux · · Score: 2, Funny

    proffered paired prime proof postulated pants

    1. Re:proffered paired prime proof poofed by HMA2000 · · Score: 4, Funny

      Previously Proffered Paired Prime Proof Pwn3d!

  17. Correcting 'proof'? by Rirath.com · · Score: 4, Funny

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

    Sounds a lot like Republicans.

  18. Good thing we are all really nerds here by Hao+Wu · · Score: 3, Insightful

    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.

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    I suggest you read Slashdot