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There Are Infinitely Many Prime Twins

Posted by michael on from the so-the-theory-goes dept.

fustflum writes "R. F. Arenstorf from Vanderbilt University has presented a 38-page possible proof of the twin-prime conjecture using methods from classical analytic number theory. The paper is on arxiv.org and is freely available to the public. Twin primes are pairs of primes where both p and p + 2 are prime. "It is conjectured that there are an infinite number of twin primes ... but proving this remains one of the most elusive open problems in number theory." More information about twin primes can be found on Mathworld."

11 of 479 comments (clear)

  1. Number theory by PHP+Wolf · · Score: 5, Funny
    but proving this remains one of the most elusive open problems in number theory

    I think we all know the most elusive open problem in number theory is "How many licks does it take to get to the center of a tootsie pop?"

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    Double Compile

    1. Re:Number theory by Da+Fokka · · Score: 5, Funny

      Reminds me of a funny story I heard at an algorithm course in college.
      Supposedly this guy thought up this new algorithm to calculate large primes in relatively short time. He was granted the use of the university mainframe. He implemented the progam and ran it.
      After a couple of days the printer started printing out the number, which was so large it needed a pack of sheets to fit on.
      Excited, he looked at the sheets to be gravely disappointed. The last digit was an 8.

      Probably an urban legend, but a nice one for sure :)

  2. I have a better proof by Anonymous Coward · · Score: 5, Funny

    but it hit /.'s maximum post size limit :(

  3. Re:This is why mathematicians are soooo popular. by servognome · · Score: 5, Funny

    "You know, mathematicians theorize that there's an infinite number of prime twins, and... hey, where are you going?"
    You would have gotten farther if you had said that without staring the whole time at her "prime twins"

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    D6 63 0D 70 89 81 BB 8E 7B 7C 5F 5D 54 EA AB 73
  4. 38 pages? by Wakkow · · Score: 5, Funny

    They should have put it in 37 pages..

  5. Well, one thing's for sure.. by robbo · · Score: 5, Funny

    they're all odd.

    (Waiting for my spot in the math hall of fame)

    --
    So long, and thanks for all the Phish
  6. Prime Arithmetic Progression also in the news by micha2305 · · Score: 5, Interesting

    Something I read in Science the other day: There's a new proof in review that there are infintely many sequences such as 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089 -- primes that differ by a constant offset. See also Mathworld.

  7. Re:One smart dude by fatphil · · Score: 5, Insightful

    Slow down!
    It's not been reviewed yet.

    I'm waiting until Granville, Odlyzko, Mihailescu, or someone similar gives it the thumbs up.
    However, it's not obvious tosh, and therefore if it does have flaws it may well be correctible, or at least provide new insight.

    The guy certainly _was_ brilliant, but given that he started his peak in the mid-60s, there's no guarantee he's still at it.

    FP.

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    Also FatPhil on SoylentNews, id 863
  8. Re:I didn't RTFA by Dominic_Mazzoni · · Score: 5, Informative

    OK, I'm too lazy to RTFA, but, if there are infinite numbers, why would there not be infinite prime numbers, and infinite prime twins? Are there also not infinite perfect numbers, or ...?

    That's a good question.

    The fact that there are an infinite number of numbers doesn't immediately imply that there are an infinite number of primes, but Euclid figured out how to prove this is true in about 300 BC. It only takes a few sentences to explain it; here's one example.

    It is definitely not obvious that there are an infinite number of twin primes. It has been an open question for more than a century, and some of the greatest minds in mathematics have worked on it. If this proof is correct, it will be a major result.

    I was trying to think of a good example of something that there is not an infinite number of. Browsing through MathWorld, I found Truncatable Primes - there are only 83 of these.

    Can anyone think of any other examples of a type of number that only has a finite number of them, even though at first glance it seems like there might be an infinite number of them?

  9. He makes a mistake... by b0r0din · · Score: 5, Funny

    Look on page 27. He's trying to integrate homeomorphic convergence using a Baxter-Bates supermodality, which Krause clearly explained is impossible for T(s) in a non-linear progression.

    Ok, just fuckin with ya. My mind wandered after I saw the word 'Abstract.' ;)

    1. Re:He makes a mistake... by Anonymous Coward · · Score: 5, Funny

      Yeah, I see a lot of people attempting to integrate homophobic conformance using Master-Bates supermoodality, which Krauds exploded as impenetrable for T/bag in a non-lesbian prostation.