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Twin Prime Proof Proffered 179

Posted by samzenpus
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."
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Twin Prime Proof Proffered

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  • Withdrawn (Score:5, Informative)

    by Agret (752467) <alias,zero2097&gmail,com> on Thursday November 04, 2004 @07:05AM (#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    The paper has since been withdrawn with the reason "A serious error has been found in the paper, specifically, Lemma 8 is incorrect."
    • So perhaps the Slashdot post should be withdrawn as well since tere is nothing new here. Move along.
    • Re:Withdrawn (Score:5, Informative)

      by metlin (258108) * on Thursday November 04, 2004 @07:18AM (#10721885) 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      • Re:Withdrawn (Score:4, Interesting)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) <sdaman@@@mindspring...om...tld> on Thursday November 04, 2004 @08:45AM (#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        • Re:Withdrawn (Score:5, Informative)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) * on Thursday November 04, 2004 @08:59AM (#10722232) 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.
        • Re:Withdrawn (Score:3, Informative)

          by metlin (258108) *
          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.
        • Because that's what good professors do. You're more likely to stay in the program if you get some exposure to the top names at the school.

          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!
      • Before they patch the problem, what are the chances that someone will develop an exploit? And will that let them root the system?
    • by kimmerin (782473)
      And who showed that Lemma 8 of the proof is incorrent? G. Tenenbaum of the Institut Élie Cartan in Nancy, so it's a French Fried Proof.
  • by Anonymous Coward on Thursday November 04, 2004 @07:05AM (#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?
  • by dabigpaybackski (772131) on Thursday November 04, 2004 @07:06AM (#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 @07:10AM (#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."
    • 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)

    by Anonymous Coward on Thursday November 04, 2004 @07:11AM (#10721863)
    The mistake was found back in June [nodak.edu]
    • Re:old news (Score:5, Interesting)

      by gnalle (125916) on Thursday November 04, 2004 @08:43AM (#10722167)
      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 :)

  • Tenenbaum? (Score:2, Funny)

    by Vo0k (760020)
    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?

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

      by nbert (785663)
      G. Tenenbaum != Andrew S. Tanenbaum
    • 50% Funny
      40% Overrated
      10% Informative

      Try getting more negative karma from a single post, trolls!
      • My reply to your post:

        A user has moderated your comment "Informative" (+1).
        It is currently scored Informative (2)

        A user has moderated your comment "Overrated" (-1).
        It is currently scored Informative (1).

        A user has moderated your comment "Insightful" (+1).
        It is currently scored Insightful (2).

        A user has moderated your comment "Insightful" (+1).
        It is currently scored Insightful (3).

        A user has moderated your comment "Overrated" (-1).
        It is currently scored Insightful (2).

        I never heard anyone shouting t

        • Tenenbaum?, posted to Twin Prime Proof Proffered, has been moderated Funny (+1).
          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
    • Not the same guy; this one appears to be royalty [imdb.com].
  • I love.... (Score:5, Funny)

    by Ingolfke (515826) on Thursday November 04, 2004 @07:12AM (#10721870) Journal
    scientists doing math,
    slashdotters aimless wrath,
    comments from stupid jerks,

    and TWINS!
  • twin primes. (Score:4, Interesting)

    by rubberbando (784342) on Thursday November 04, 2004 @07:34AM (#10721937)
    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. (Score:1, Insightful)

      maximum and minimums grow ever higher
      It's maxima and minima. And I would have thought that the latter tend to grow ever lower...
      • 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?
    • Re:twin primes. (Score:3, Informative)

      by fymidos (512362)
      >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.
      • The actual proof that there are infinite primes is more complex. But here's a simplified version which I stole word for word from from Harald Tveit Alvestrand.

        ASSUME that the number of primes is finite.

        THEN IN THEORY, one could list them all, forming "the set of all primes". Then, we can multiply them together, and add 1 to the result.

        The resulting number is obviously (by rules of mathematics):
        - Not any of the known primes, since it is larger than them all
        - Not divisible by any of the known primes,

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

      by isometrick (817436) on Thursday November 04, 2004 @08:09AM (#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!
    • Re:twin primes. (Score:1, Interesting)

      by Lifewish (724999)
      Good summary from a waveform perspective [maths.org].
      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.
      • 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.
        • If a complete list of existing primes is specified and a number is not divisible by any of these then whether we say that it is prime or has unknown prime factors is completely irrelevant as the contradiction has already been broached.
          • That is true. Nevertheless, you made the additional claim that a certain number was prime, and used that FALSE claim to arrive at your contradiction. Your proof was incomplete, so I corrected it.
            • Yeah, the phrasing was a bit dodgy. On the other hand, it's equally dodgy to say that the number p1*p2*...*pn + 1 is the product of other primes since our assumption is that there are no other primes. Your proof and my proof are effectively equivalent, given that the contradiction kicks in before we have to decide what our "new primes" will be.
      • p1*p2*...*pn + 1 isn't necessarily prime (for example n = 4 gives 2 * 3 * 5 * 7 + 1 = 211 = 13 * 16). But if isn't then it must be divisible by prime other than p1, ..., pn so you've still got the contradiction.
    • Re:twin primes. (Score:4, Interesting)

      by Kjella (173770) on Thursday November 04, 2004 @08:43AM (#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
      • 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.
        • 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?
      • "All it proves is that there's a prime q <= p1*p2*....*p999*p1000+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.
        • Read it more carefully. Your example is correct, but not a counter example to what he actually claimed (a prime q less than or equal 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)

        by Rufus88 (748752)
        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.
    • 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.
    • "The Music of The Primes" by Marcus du Sautoy, Harper Collings 2004.
      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
    • There is no upper bound on the maximum gap between primes. The proof is quite easy: there are (N - 1) consecutive composite numbers from (N! + 2) to (N! + N). This is because 2 divides N! + 2; 3 divides N! + 3, and so on. So if you want a billion consecutive composite numbers, such a sequence starts at (1,000,000,001! + 2).

      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

  • by bearnol (259150) on Thursday November 04, 2004 @07:36AM (#10721946)
  • Poor hyperlinking (Score:3, Insightful)

    by BarryNorton (778694) on Thursday November 04, 2004 @07:47AM (#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...
  • by D-Cypell (446534) on Thursday November 04, 2004 @07:53AM (#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 @08:17AM (#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."

    • by Lifewish (724999) on Thursday November 04, 2004 @08:26AM (#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

        • Engineers think that equations imitate reality
          Physicists think that reality imitates equations
          Mathematicians can't make the connection
        • Math jokes, huh? Ok, I'm game.

          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."

    • by Anonymous Coward
      And here's how to confuse a mathematician:

      Let odds be even...

  • by Rirath.com (807148) on Thursday November 04, 2004 @11:50AM (#10724020)
    "however mathematicians remain hopeful that the proof can be corrected."

    Sounds a lot like Republicans.
  • by Hao Wu (652581) on Thursday November 04, 2004 @11:53AM (#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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