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There Are Infinitely Many Prime Twins
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."
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.
Also FatPhil on SoylentNews, id 863
"Hopefully this new paper will have some good cryptographic applications"
It won't. Sorry. Just like AKS, this is something that's entirely in the realm of the theoretical.
FP.
Also FatPhil on SoylentNews, id 863
Have you never heard of Tom Lehrer? If not, shame on you.
> 2. Given: A certain positive percentage of primes differ by two.
Not necessarily true. It's equally possible that a certain finite number of primes differ by two, not an infinite percentage of primes.
Give me my cookie now.
- For the complete works of Shakespeare: cat
It's quite easy to write a program that will verify any proof written out in formal logic.
The problem is that to write out any proof that isn't really obvious anyway in formal logic requires huge amounts of time and space (think 3000+ pages rather than 38, mainly proving the equivalent of 2+2=4).
There are a few people trying to produce a language for mathematics that a computer can understand and check which isn't quite so completely painful and allows you to quote theorems; but they're still quite messy and most of the theorems you might want to use haven't been included yet.
So people go for the time-honoured method of writing proofs in a way that makes sense to a human, and then having people check the logic by hand. Then you need someone who works in the same field to verify it, because people working in different fields won't know the theorems and would have to spend a year or so learning the background.
The reason people don't want to assume something is true until it's been checked is that if you assume that X's proof of a theorem is valid, and you then produce a 200-page proof of the Riemann Hypothesis which assumes the theorem X said he'd proved, then someone checks X's proof and finds a mistake, your proof also collapses.