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Major Advance Towards a Proof of the Twin Prime Conjecture
ananyo writes "Researchers hoping to get '2' as the answer for a long-sought proof involving pairs of prime numbers are celebrating the fact that a mathematician has wrestled the value down from infinity to 70 million. That goal is the proof to a conjecture concerning prime numbers. Primes abound among smaller numbers, but they become less and less frequent as one goes towards larger numbers. But exceptions exist: the 'twin primes,' which are pairs of prime numbers that differ in value by 2. The twin prime conjecture says that there is an infinite number of such twin pairs. Some attribute the conjecture to the Greek mathematician Euclid of Alexandria, which would make it one of the oldest open problems in mathematics. The new result, from Yitang Zhang of the University of New Hampshire in Durham, finds that there are infinitely many pairs of primes that are less than 70 million units apart. He presented his research on 13 May to an audience of a few dozen at Harvard University in Cambridge, Massachusetts. Although 70 million seems like a very large number, the existence of any finite bound, no matter how large, means that that the gaps between consecutive numbers don't keep growing forever."
You've misunderstood the proof as a test to see whether a subset of primes up to prime n is complete. That's not the case. You start by taking the entire postulated finite set of primes.
The condradiction you receive - that it's possible to create a prime outside of the complete set of all primes - indicates that any finite set is incomplete. (Or alternatively that addition, multiplication, or sets work very differently than we assume, but let's stick to the form of mathematics the problem addresses.)
No kidding!!! What do you say at this point?
So in addition to giants, there are great people standing on the shoulders of there own communities, too? That is somehow comforting.
It's shoulders all the way down.
Um, one question that a person could ask is: If this proof is found, how does it change the world? How would being able to use the proof influence something in the real world? I'm not saying it can't or won't, only that simply picking a brainy subject does not mean that doing things in it aren't basically intellectual masturbation.
The change to our world is this: we now know something that we didn't know before. Now we can teach this new knowledge to others (and by others I mean people smarter than me) who can find new places and ways to apply this new knowledge. They might never do anything interesting with it, or it might cause an avalanche of new findings, we don't know. But we, as a species, fundamentally know more today than we did yesterday.
As an example, the ancient greeks studied prime numbers. Was there any immediate use of primes at the time? Did it allow them to improve harvest? Defeat the Roman army? Nope, they just studied them. At the time there is no way that they could have conceived their application for encryption. Yet today, all commerce on the web uses the mathematics of primes.
It is not important to have an immediate use for knowledge.
It's shoulders all the way down.
You were probably going for funny, but if I had mod points I'd call this insightful. It really is shoulders all the way down; no one accomplishes anything of significance without relying on many, many others.
Note to ACs: I usually delete AC replies without reading them. If you want to talk to me, log in.
Yes, but if you read the article, or hell, even the summary, then you'd know it was about primes.
Some AC felt the need to make a lame '42' reference. Then, against all odds, it somehow managed to get back around to being on topic when someone else gave it a -1, thus rendering it a nicely prime 41. Then you came along and decided to be an ass. Well done.
But wait! With 41 you don't just get an "on topic" prime number. You'll also find that 41 is actually a twin in the twin prime pair of (41, 43)! That's right, it is completely on topic... so.... nah nah nahnah nah.
Now, as far as I can tell I've managed to make two relevant posts on the topic out of a seemingly impossible "42 duh duh" comment. On the other hand, you've managed only to be an asshole and contribute nothing other than bad karma. As far as you comment about making more money goes, I'm confused, who knows, maybe I got whooshed or missed a meme or something. Or maybe I've just been trolled. But, maybe you'd make more if you weren't such an asshole and instead just let people have a good time without trying to piss on 'em. Especially when it doesn't even matter.
My present is the activity I am currently engaged in with the purpose of turning the future into a better past.