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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."

4 of 479 comments (clear)

  1. 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.

  2. Other Number Theory Tricks? by CoolGuySteve · · Score: 4, Interesting

    The sum of any two consecutive odd numbers is divisible by 4. I misread a question in first year and proved it.

    I thought that was fairly neat, it makes me the life of the party when I tell it to people. (Well, not really. Depressing.) Does anyone know any other little tricks like that?

  3. amazing if it's true by cancerward · · Score: 4, Interesting
    The author received his doctorate 48 years ago. According to MathSciNet his first paper was in 1963, and his most recent in 1993.

    If it turns out to be true, this will be super-duper-extraordinary - the man is probably in his 70s. G. H. Hardy wrote: "No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game". Wiles proved FLT at 40, Perelman of the purported Poincare proof is in his 30s... this is similar-level stuff. The only thing I can think of that even comes close is Fred Galvin in his 50s (?) proving the Dinitz conjecture.

    You can follow discussions on sci.math and fr.sci.maths. Or read about how similar asymptotic proofs about properties of primes failed. Remember, this is arxiv - in the age of electronic preprints, you get many good proofs like Perelman's along with almost-proofs like Castro-Mahecha's and Dunwoody's.

  4. Re:What about prime triplets? by Sigma+7 · · Score: 4, Interesting
    3, 5, 7?
    There is only one set of prime triplets where the numbers are seperated by 2. There are no other triplets because at least one number in that triplet is a multiple of 3. (The numbers being X, X+2, and X+4. Using modular arithmtic to cap the additives would therefore require all numbers of the set X, X+2 and X+1 to not be a multiple of three, which isn't really possible because of how Integer numers work.)

    Or prime siblings that are seperated by numbers other than 2?
    To find an infinite number of prime siblings, you first need to find an appropriate set of numbers. To cut down on processing time, you should note that these numbers are seperated by 6, or a multiple thereof.