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!

## Comments