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Twin Prime Proof Proffered

Posted by samzenpus on Thu Nov 04, 2004 06:00 AM
from the is-this-going-to-be-on-the-test dept.
Education Science
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."
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  • Withdrawn (Score:5, Informative)

    by Agret (752467) <alias DOT zero2097 AT gmail DOT com> on Thursday November 04 2004, @06:05AM (#10721842) Homepage Journal
    The paper has since been withdrawn with the reason "A serious error has been found in the paper, specifically, Lemma 8 is incorrect."

    • Re:Withdrawn (Score:5, Informative)

      by metlin (258108) * <narayan@fas.harC ... minus herbivore> on Thursday November 04 2004, @06:18AM (#10721885) Homepage Journal

      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      • Re:Withdrawn (Score:4, Interesting)

        by gartogg (317481) <<dlt.mo.gnirpsdnim> <ta> <namads>> on Thursday November 04 2004, @07:45AM (#10722174) Homepage Journal
        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        • Re:Withdrawn (Score:5, Informative)

          by metlin (258108) * <narayan@fas.harC ... minus herbivore> on Thursday November 04 2004, @07:59AM (#10722232) Homepage Journal
          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?
      • Props for Bellissard. I'm going to his Calc. II Honors lecture in 30 minutes. Why he was chosen to teach the clueless freshmen, I don't know. He probably has better things to do than watch us stare blankly back at him.
        • 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.

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

    by Anonymous Coward on Thursday November 04 2004, @06:05AM (#10721844)
    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?

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

    by dabigpaybackski (772131) on Thursday November 04 2004, @06:06AM (#10721848) Homepage
    Who's that weird janitor kid who keeps doing equations on the hallway chalkboards? Maybe he could help out with this.

  • /. version (Score:5, Funny)

    by cheezemonkhai (638797) on Thursday November 04 2004, @06:10AM (#10721860) Homepage
    "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 (Score:5, Informative)

    by Anonymous Coward on Thursday November 04 2004, @06:11AM (#10721863)
    The mistake was found back in June [nodak.edu]

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

      by gnalle (125916) on Thursday November 04 2004, @07:43AM (#10722167) Homepage
      A simple Google search [google.com] reveals that the story is a dupe [slashdot.org]. 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 :)

  • 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?

  • I love.... (Score:5, Funny)

    by Ingolfke (515826) on Thursday November 04 2004, @06:12AM (#10721870) Journal
    scientists doing math,
    slashdotters aimless wrath,
    comments from stupid jerks,

    and TWINS!
    • That is just beautiful! This deserves more than +5 funny as it is the best post I've read on /. in months...

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

  • twin primes. (Score:4, Interesting)

    by rubberbando (784342) on Thursday November 04 2004, @06:34AM (#10721937) Homepage
    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?
    • >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)
      • 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:4, Informative)

      by isometrick (817436) on Thursday November 04 2004, @07:09AM (#10722043)
      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!
      • 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]?
          • 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!
      • 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.
      • The site seems to still be available at the Web Archive [archive.org]:

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

      by Kjella (173770) on Thursday November 04 2004, @07:43AM (#10722168) Homepage
      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
      • 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.
      • Since the gap between two primes cannot get smaller than the gap between 2 and 3 (i.e. no number in between at all), the minimum gap is actually a constant function as soon as you passed 3 (and undefined before, of course).

        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?
      • 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.

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

    by bearnol (259150) on Thursday November 04 2004, @06:36AM (#10721946)
    http://www.bearnol.pwp.blueyonder.co.uk/Math/wanle ss2.html [blueyonder.co.uk]
    • Wow. That site seems to have a lot of other cool stuff, too. Thanks!

      I'm guessing you're probably not the same James Wanless as the tarot reader/whatever?
        • No sarcasm intended, merely meant it as a compliment. Noticed that the upper directory [blueyonder.co.uk] had a lot of other cool math stuff, too.

          (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?

  • Poor hyperlinking (Score:3, Insightful)

    by BarryNorton (778694) on Thursday November 04 2004, @06:47AM (#10721973)
    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...

  • Serious Error.. (Score:4, Funny)

    by D-Cypell (446534) on Thursday November 04 2004, @06:53AM (#10721993)
    [i]it seems that a hole has recently been found in the proof[/i]

    He forgot to carry the 1
  • News that's only 5 months out-of-date.

  • Math humor (Score:4, Funny)

    by Brian Kendig (1959) on Thursday November 04 2004, @07:17AM (#10722078) Homepage
    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... (Score:5, Funny)

      by Lifewish (724999) on Thursday November 04 2004, @07:26AM (#10722109) Homepage Journal
      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.
      • 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

        • You, my friend, must be a mathematician, because only a mathematician would say that "you can prove anything from a contradiction". You are clearly confused, seeing as you don't see how this statement would confuse a mathematician. It seems to work...

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

    by Rirath.com (807148) on Thursday November 04 2004, @10:50AM (#10724020)
    "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)

    by Hao Wu (652581) on Thursday November 04 2004, @10:53AM (#10724082) Homepage
    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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