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(Yahoo)   Connection between prime numbers has been proven, there will be math   (news.yahoo.com) divider line 46
    More: Interesting, prime numbers, theorems, number theory, Kyoto University, unified theory, The Sciences, not proven, integers  
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7017 clicks; posted to Geek » on 11 Sep 2012 at 4:22 PM (2 years ago)   |  Favorite    |   share:  Share on Twitter share via Email Share on Facebook   more»



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2012-09-11 03:15:30 PM  
Math porn.

/ giggity.
 
2012-09-11 03:31:38 PM  
I already solved it one night at work. I was mopping the hall and saw the problem on the board, and no one was looking, so...I just solved that shiat.

Then I banged Minnie Driver, asked some douche about apples, then cried to Robin Williams.

Then I ran away from home.

Good times.
 
2012-09-11 03:40:16 PM  
Any farkers want to explain how this could impact reality, and/or make Math tests even harder?
 
2012-09-11 03:52:35 PM  
greenobles.com

Just got a clit boner.
 
2012-09-11 03:53:06 PM  

Spad31: I already solved it one night at work. I was mopping the hall and saw the problem on the board, and no one was looking, so...I just solved that shiat.

Then I banged Minnie Driver, asked some douche about apples, then cried to Robin Williams.

Then I ran away from home.

Good times.


24.media.tumblr.com
 
2012-09-11 04:08:28 PM  
Well, I read that. Yep.
 
2012-09-11 04:28:57 PM  
dammit. Now they will go and factor my RSA based PGP key


/yeah, I use gpg, but I made the key back in the day
 
2012-09-11 04:36:02 PM  
um.....

Neat.

Number theory makes my brain hurt.

//Hot mathematicians are hotter than hot librarians. I dare someone to prove me wrong.
 
2012-09-11 04:40:04 PM  

meat0918: //Hot mathematicians are hotter than hot librarians. I dare someone to prove me wrong


I suggest we suspend the normal rules for proving things in this thread and allow Proof by Lots of Specific Cases.
 
2012-09-11 04:45:49 PM  

meat0918: um.....

Neat.

Number theory makes my brain hurt.

//Hot mathematicians are hotter than hot librarians. I dare someone to prove me wrong.


Depends on what you want out a relationship. Mathematicians are better at multiplication, but librarians are stacked.
 
2012-09-11 04:51:16 PM  

Grand_Moff_Joseph: Any farkers want to explain how this could impact reality, and/or make Math tests even harder?


Check the 2nd paragraph

The proof will also have ramifications all over mathematics, and even in the real-world field of data encryption.
 
2012-09-11 04:54:57 PM  

Baryogenesis: nd even in the real-world field of data encryption.


A lot of current encryption schemes rely on the fact that large primes are a PITA to calculate... if they were no longer so, a lot of our protection would go from "that'll take hundreds of years to break!" to "hey look, China's already broken it!"
 
2012-09-11 04:55:19 PM  
Part 1
Part 2
Part 3
Part 4

Good luck, farkers.
 
2012-09-11 04:57:22 PM  

Grand_Moff_Joseph: Any farkers want to explain how this could impact reality, and/or make Math tests even harder?


Take this with a grain of salt as I can not back it up in the slightest.

I remember reading that really really long prime numbers were valuable in some regard in the realm information security or some such. Basically, because they are unique there is no formula to brute force? I believe it was something like that.

So if they can come up with some sort of formula, they are no longer special?
 
2012-09-11 05:01:07 PM  

Grand_Moff_Joseph: Any farkers want to explain how this could impact reality, and/or make Math tests even harder?


Public-key encryption (the form of encryption used by secure websites and such) is dependent on each side of the transaction having a key from a predetermined pair -- one public, one private.

The heart of the public key is basically a huge honkin' number that is used to encrypt the data -- and the number is the product of two large prime numbers. This means that the only factors of the number at the heart of the public key are: itself, 1, and the two primes that created it.

The heart of the private key that decrypts the message is the two primes that were used to make the public key.

What makes the system secure is that since there is no proven pattern to primes, you can only crack the public key into its components by sheer brute force. Other than the known primes, to even get a prime number you have to take [NUMBER_X] and keep trying to factor it out with larger and larger numbers to determine whether or not it's actually a prime, then (if it is prime) divide the public key by this number to see if you get an integer.

So, if you take some hundreds-of-digits public key number that is the product of exactly two large primes, you have to start generating, and then testing, prime numbers one by one to determine whether it is a factor in the huge honkin' number. Of course, once you can figure one of them out, you can figure out the other one... but you still have to sort through finding a number that is beyond enormous to find even one of them, and on average that will take you longer than the age of the universe to do.

If this theorem leads to an algorithm that allows people to generate primes rapidly rather than by brute force, that compromises the security of private keys. It means that the "seeking out large primes for testing" portion of the attack can be handled in a greatly reduced time.

/Not a mathematician or a security expert -- I may be wrong in some parts.
 
2012-09-11 05:05:59 PM  
I guess we can hope that determining whether a number is square free is at least as hard as testing its a prime

Wolfram-Alpha says "There is no known polynomial time algorithm for recognizing squarefree integers or for computing the squarefree part of an integer. In fact, this problem may be no easier than the general problem of integer factorization (obviously, if an integer n can be factored completely, n is squarefree iff it contains no duplicated factors)."

So maybe the RSA algorithm isn't totally farked.
 
2012-09-11 05:08:31 PM  
Well, I think most mathematicians would tell you that they believed there must be a way to resolve primes formulaically, we just don't (didn't) know what it is (was). That said, any decent mathematician will also tell you that anything and everything can be derived formulaically.
 
2012-09-11 05:18:32 PM  
The proof is huge - it is broken up into these papers

Mochizuki, S.- Inter-universal teichmuller theory I: construction of Hodge Theatres (2012). available at http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmull e r%20Theory%20I.pdf

Mochizuki, S.- Inter-universal teichmüller theory II: Hodge-Arajekekiv-theoretic evalulation (2012). available at http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmull e r%20Theory%20II.pdf

Mochizuki, S. - Interuniversal teichmüller theory III: canonical splittings of the log-theta-lattice (2012). available at http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmull e r%20Theory%20III.pdf

Mochizuki, S.- Interuniversal teichmüller theory IV: log-volume computations and set-theoretic foundations (2012). available at http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmull e r%20Theory%20IV.pdf

In addition very few mathematicians in the world are qualified to understand the proof.
 
2012-09-11 05:26:52 PM  

HairBolus: The proof is huge - it is broken up into these papers

Mochizuki, S.- Inter-universal teichmuller theory I: construction of Hodge Theatres (2012). available at http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmull e r%20Theory%20I.pdf

Mochizuki, S.- Inter-universal teichmüller theory II: Hodge-Arajekekiv-theoretic evalulation (2012). available at http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmull e r%20Theory%20II.pdf

Mochizuki, S. - Interuniversal teichmüller theory III: canonical splittings of the log-theta-lattice (2012). available at http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmull e r%20Theory%20III.pdf

Mochizuki, S.- Interuniversal teichmüller theory IV: log-volume computations and set-theoretic foundations (2012). available at http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmull e r%20Theory%20IV.pdf

In addition very few mathematicians in the world are qualified to understand the proof.


i0.kym-cdn.com
 
2012-09-11 05:33:10 PM  

Spad31: I already solved it one night at work. I was mopping the hall and saw the problem on the board, and no one was looking, so...I just solved that shiat.


www.smbc-comics.com
 
2012-09-11 05:33:55 PM  
Also:

www.smbc-comics.com
 
2012-09-11 05:34:54 PM  

BKITU: Grand_Moff_Joseph: Any farkers want to explain how this could impact reality, and/or make Math tests even harder?

Public-key encryption (the form of encryption used by secure websites and such) is dependent on each side of the transaction having a key from a predetermined pair -- one public, one private.

The heart of the public key is basically a huge honkin' number that is used to encrypt the data -- and the number is the product of two large prime numbers. This means that the only factors of the number at the heart of the public key are: itself, 1, and the two primes that created it.

The heart of the private key that decrypts the message is the two primes that were used to make the public key.

What makes the system secure is that since there is no proven pattern to primes, you can only crack the public key into its components by sheer brute force. Other than the known primes, to even get a prime number you have to take [NUMBER_X] and keep trying to factor it out with larger and larger numbers to determine whether or not it's actually a prime, then (if it is prime) divide the public key by this number to see if you get an integer.

So, if you take some hundreds-of-digits public key number that is the product of exactly two large primes, you have to start generating, and then testing, prime numbers one by one to determine whether it is a factor in the huge honkin' number. Of course, once you can figure one of them out, you can figure out the other one... but you still have to sort through finding a number that is beyond enormous to find even one of them, and on average that will take you longer than the age of the universe to do.

If this theorem leads to an algorithm that allows people to generate primes rapidly rather than by brute force, that compromises the security of private keys. It means that the "seeking out large primes for testing" portion of the attack can be handled in a greatly reduced time.

/Not a mathematician or a security expert -- I may be wr ...


I read that in Keith Devlin's voice.
 
2012-09-11 05:47:17 PM  
Ok, a lot of FUD in this thread, so...

A) Generating primes for RSA keys is already incredibly efficient. Get a range of numbers you want that is random and storable (i.e., some random 1024 bit number A, your range is (A, A+2^20) or whatever), sieve out the smaller prime factors, test the rest with the Miller-Rabin primality test, then test the remainders with AKS if you want to be 100% sure. Repeat with another random start. Note, this does not help you crack an RSA public key, this is to generate one.
B) Fast enumeration of primes will not help you crack an RSA key any, the search space is still too freakin huge. But you also don't need to "brute force" it. The Number Field Sieve is the best approach in existence, and it is exponentially faster than a brute force search, but still too slow for large keys.
 
2012-09-11 05:49:51 PM  

Mytch: ...any decent mathematician will also tell you that anything and everything can be derived formulaically.


A decent mathematician that disagrees:
upload.wikimedia.org
 
2012-09-11 05:52:50 PM  

Faraday's Child: Mytch: ...any decent mathematician will also tell you that anything and everything can be derived formulaically.

A decent mathematician that disagrees:
[upload.wikimedia.org image 212x270]


Personally, I hope he's right.
 
2012-09-11 06:08:06 PM  
i3.kym-cdn.com
 
2012-09-11 06:12:19 PM  
But I was told.... ah, forget it.

The diagram that accompanied TFA made me think the mathematician read Sphere too many times.
 
2012-09-11 06:28:10 PM  

incendi: meat0918: //Hot mathematicians are hotter than hot librarians. I dare someone to prove me wrong

I suggest we suspend the normal rules for proving things in this thread and allow Proof by Lots of Specific Cases.



Oh, you mean the proof to the four color theorem.

/Esoteric math joke.
 
2012-09-11 06:43:45 PM  
But is it a breakthrough of Gaussian proportions?

//Happy 20th birthday to Sneakers! Released Sept. 10th, 1992.
 
2012-09-11 06:52:08 PM  
It would take me to the end of eternity to type all that out. I don't even have most of those characters on my keyboard.
 
2012-09-11 08:38:30 PM  

meat0918: um.....

Neat.

Number theory makes my brain hurt.

//Hot mathematicians are hotter than hot librarians. I dare someone to prove me wrong.


If you and I are to keep this on a professional level we will have to agree to disagree. Nothing is hotter than a naughty brunette librarian in glasses....I've given this way too much thought to be wrong.
 
2012-09-11 09:03:02 PM  
And this will help me win my fantasy football league how?

It won't?

Stupid nerds.
 
2012-09-11 09:21:12 PM  
i172.photobucket.com
 
2012-09-11 10:08:43 PM  

MaxSupernova: meat0918: um.....

Neat.

Number theory makes my brain hurt.

//Hot mathematicians are hotter than hot librarians. I dare someone to prove me wrong.

If you and I are to keep this on a professional level we will have to agree to disagree. Nothing is hotter than a naughty brunette librarian in glasses....I've given this way too much thought to be wrong.



No, you are wrong. And very naughty.
 
2012-09-11 10:40:03 PM  
Came for Danica McKellar pics.

I'll be ready to go again in like 10 minutes, would you like a sandwich?
 
2012-09-11 11:45:35 PM  
Yeah I'm not going to read that.
 
2012-09-12 12:12:00 AM  
Vihart?

nope dang it!
 
2012-09-12 12:53:13 AM  
so he broke the internet? this is why we can't have nice things...

/no more secrets
 
2012-09-12 12:58:50 AM  
So if this holds up, it could mean that RSA suddenly becomes a lot weaker. But does anyone know if it would cause any problems for DSA (which is based on the difficulty of discrete logarithms rather than prime numbers)? I seem to remember that the math is similar enough that an exploit in one would likely translate to the other pretty easily, but I can't claim to understand how it works.
 
2012-09-12 01:54:18 AM  
This should have no effect on RSA/prime modulation factoring encrption schemes. Indeed, it doesn't even give a "decoding" of the primes. If true, it at best says that there is no easy way to generate large primes because they are "well hidden" from simple arithmetic using known primes.

And please, read this and tell me this guy isn't just a crack-pot playing games with the math-geeks:

Abstract. The present paper is the first in a series of four papers, the
goal of which is to establish an arithmetic version of Teichm¨uller theory for number
fields equipped with an elliptic curve - which we refer to as "inter-universal
Teichm¨uller theory" - by applying the theory of semi-graphs of anabelioids,
Frobenioids, the ´etale theta function, and log-shells developed in earlier papers by
the author. We begin by fixing what we call "initial Θ-data", which consists of
an elliptic curve EF over a number field F, and a prime number l ≥ 5, as well as
some other technical data satisfying certain technical properties. This data determines various hyperbolic orbicurves that are related via finite ´etale coverings to the
once-punctured elliptic curve XF determined by EF . These finite ´etale coverings
admit various symmetry properties arising from the additive and multiplicative
structures on the ring Fl = Z/lZ acting on the l-torsion points of the elliptic curve.
We then construct "Θ±ell
NF-Hodge theaters" associated to the given Θ-data. These
Θ±ell
NF-Hodge theaters may be thought of as miniature models of conventional
scheme theory in which the two underlying combinatorial dimensions of a
number field - which may be thought of as corresponding to the additive and
multiplicative structures of a ring or, alternatively, to the group of units and
value group of a local field associated to the number field - are, in some sense,
"dismantled" or "disentangled" from one another. All Θ±ell
NF-Hodge theaters
are isomorphic to one another, but may also be related to one another by means of a
"Θ-link", which relates certain Frobenioid-theoretic portions of one Θ±ell
NF-Hodge
theater to another is a fashion that is not compatible with the respective conventional ring/scheme theory structures. In particular, it is a highly nontrivial
problem to relate the ring structures on either side of the Θ-link to one another. This
will be achieved, up to certain "relatively mild indeterminacies", in future papers
in the series by applying the absolute anabelian geometry developed in earlier
papers by the author. The resulting description of an "alien ring structure" [associated, say, to the domain of the Θ-link] in terms of a given ring structure [associated,
say, to the codomain of the Θ-link] will be applied in the final paper of the series to
obtain results in diophantine geometry. Finally, we discuss certain technical results
concerning profinite conjugates of decomposition and inertia groups in the tempered fundamental group of a p-adic hyperbolic curve that will be of use in the
development of the theory of the present series of papers, but are also of independent
interest.


I realize English may not be his first language, but there is no way that he needs that much self-created jargon to explain what he is doing.
 
2012-09-12 04:05:54 AM  
FTA: If Shinichi Mochizuki's 500-page proof stands up to scrutiny

Christ. And I thought my proofs homework was tedious...
 
2012-09-12 05:06:23 AM  
I've always been fascinated by prime numbers and have long suspected there is a pattern there. The spiral pattern that illustrates this article is something I discovered for myself, although what it means I have not the slightest clue, let along being equipped to do a formal mathematical proof of anything. Like most people, my math gives up in the XVIIth century.

Still, it is nice to know I was sorta on to something, vaguely. Whatever it was.
 
2012-09-12 05:15:22 AM  
Obvious.
www.timecube.com
 
2012-09-12 07:15:16 AM  

iawai: This should have no effect on RSA/prime modulation factoring encrption schemes. Indeed, it doesn't even give a "decoding" of the primes. If true, it at best says that there is no easy way to generate large primes because they are "well hidden" from simple arithmetic using known primes.

And please, read this and tell me this guy isn't just a crack-pot playing games with the math-geeks:

Abstract. The present paper is the first in a series of four papers, the
goal of which is to establish an arithmetic version of Teichm¨uller theory for number
fields equipped with an elliptic curve - which we refer to as "inter-universal
Teichm¨uller theory" - by applying the theory of semi-graphs of anabelioids,
Frobenioids, the ´etale theta function, and log-shells developed in earlier papers by
the author. We begin by fixing what we call "initial Θ-data", which consists of
an elliptic curve EF over a number field F, and a prime number l ≥ 5, as well as
some other technical data satisfying certain technical properties. This data determines various hyperbolic orbicurves that are related via finite ´etale coverings to the
once-punctured elliptic curve XF determined by EF . These finite ´etale coverings
admit various symmetry properties arising from the additive and multiplicative
structures on the ring Fl = Z/lZ acting on the l-torsion points of the elliptic curve.
We then construct "Θ±ell ...

I realize English may not be his first language, but there is no way that he needs that much self-created jargon to explain what he is doing.


I don't know, it seems plausible to me. Mathematics really is pretty much a seperate language, and if there were an easy, simple, clear way to express the ideas in the proof...well, someone owuld have figured it out by now.
/Always heard that for pure math programs in college the Verbal SAT score counts more than the Math SAT score 

//Oh, also, why do you think the jargon is "self created"? I recognized a lot of individual terms from high school calculus class, even if I have no clue what they mean in the context of this proof. Unless by "self created" you meant "field (math) specific"
 
2012-09-12 12:45:08 PM  

iawai: I realize English may not be his first language, but there is no way that he needs that much self-created jargon to explain what he is doing.


What part of that abstract do you think is "self-created jargon"? Most of that language uses well defined mathematical terminology, While he introduces the notion of "inter-universal Teichmüller theory" that is just a version of Teichmüller theory. He also introduces the notion "Hodge theater" which I presume has something to do with Hodge theory. He probably creates some additional terms along these lines.

Advanced mathematics involves all sorts of abstract constructions and people need names to refer to them. I'm sorry that his attempted proof cannot be expressed in a vocabulary that you understand, but your understanding problem is not so much as with the words but with the concepts behind them.
 
2012-09-12 04:20:59 PM  

HairBolus: I'm sorry that his attempted proof cannot be expressed in a vocabulary that you understand


One Square Free Number! Two Square Free Number! AH AH AH!

www.infinitydish.com
 
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