A Slashdot post pointed me to this purported proof by Vanderbilt University's Richard Arenstorf of the Twin-Prime Conjecture, which states that there are infinitely many primes of the form P, P+2,
e.g, 5 and 7, 11 and 13, 17 and 19, or 29 and 31. This supposed proof,
if correct, would be one of the most exciting results in number theory
in quite some time. I'm not and never have been an analytic number
theorist, and I can't say that I've ever heard of Mr. Arenstorf before
today, so I'm in no position to assess the likelihood that his proof
isn't just stuff and nonsense, at least not without getting a chance to
actually read it through. Going from the comments of some of the Slashdot
readers, this guy got his PhD 48 years ago, and hit his productive
prime in the 1960s; prior to this, his most recent published paper was
in 1993. This hardly makes one feel confident in the correctness of his
work, as mathematics is notorious for being a young man's game, the
likes of Paul Erdos aside. As another commenter noted, I'd feel far
more confident that this guy's hit the mark if the likes of Peter
Sarnak, Andrew Granville, Andrew Odlyzko or Preda Mihailescu were to
give his paper a preliminary thumbs up - that would still be no
guarantee that Arenstorf was correct, of course, but it would lessen
the odds of his being wrong considerably.
One thing I noticed in the abstract of the paper was that Arenstorf
claimed that his proof depended only on methods from classical analytic
number theory, and a quick scan through suggests that this is indeed
the case, as it seems to lean most heavily on the theory of generating functions.
This leads me to harbor some hope that I really will be able to read
through the whole thing if I have the requisite patience - now all(!) I
have to do is find the necessary free time!
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