First proof that infinitely many prime numbers come in pairs. - Polidicks

[QUOTE]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 [B]without relying on unproven conjectures[/B]. Source: [URL]http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989[/URL][/QUOTE] What a boss.

Are there any practical applications to this or is it just cool math stuff?

[QUOTE=Liem;40645826]Are there any practical applications to this or is it just cool math stuff?[/QUOTE] Finding ever-larger prime numbers has serious implications for cryptography [editline]14th May 2013[/editline] I wonder what the actual value is: I doubt that it's actually exactly 70 000 000.

[QUOTE=Elecbullet;40645903]Finding ever-larger prime numbers has serious implications for cryptography [editline]14th May 2013[/editline] I wonder what the actual value is: I doubt that it's actually exactly 70 000 000.[/QUOTE] I don't think this has anything to do with cryptography. If there are any applications they will become clear later anyway.

[QUOTE=Liem;40645826]Are there any practical applications to this or is it just cool math stuff?[/QUOTE] Probably only cool math at this point but at some point in the future it might contribute to faster algorithms or something of that nature.

Interesting but not nearly as cool as a proof of infinitely many twin primes.

I don't know what any of this means

[QUOTE=Krinkels;40645939]I don't think this has anything to do with cryptography. If there are any applications they will become clear later anyway.[/QUOTE] Cryptography relies heavily on very large primes. If we know more about the nature of prime numbers, we may be able to develop better encrypting algorithms.

[QUOTE=Elecbullet;40645903]Finding ever-larger prime numbers has serious implications for cryptography[/QUOTE] This won't help you find primes at all though.

[QUOTE=ThisIsTheOne;40647228]This won't help you find primes at all though.[/QUOTE] The more we understand prime numbers, the closer we are to finding larger ones.

why are prime numbers so important

[QUOTE=Tiersin;40647050]Cryptography relies heavily on very large primes. If we know more about the nature of prime numbers, we may be able to develop better encrypting algorithms.[/QUOTE] if we know more about the nature of prime numbers, it would probably break our encrypting algorithms. shor's algorithm, for example, will make modern encryption obsolete.

[QUOTE=sYnced;40647777]why are prime numbers so important[/QUOTE] they're useful numbers

[QUOTE=sYnced;40647777]why are prime numbers so important[/QUOTE] they take a lot of cpu to find because there is no simple way to do it without quantum computing. it makes encryption easy. you have a public key that is the product of two very large prime numbers, and a secret key that is the two prime factors. you give out the public key and people are able to use it to encrypt a message to you, but no one will be able to decrypt it because they don't have the prime factors, and it would take ages on a classical computer to find the prime factors. [editline]15th May 2013[/editline] how is this wrong guys? that's how rsa works isn't it? [editline]15th May 2013[/editline] [url]http://en.wikipedia.org/wiki/RSA_%28algorithm%29#Key_generation[/url] i'm not a cryptographer so my explanation was pretty basic, but at least this form of encryption relies on prime factorization being difficult.

my head hurts, i must be an idiot

[QUOTE=Octocow;40646943]I don't know what any of this means[/QUOTE] Twin primes are two prime numbers that are only 2 apart like 3 and 5 I got this from the article it's not like I actually know things

[media]http://www.youtube.com/watch?v=Szg2DCogEW8[/media]

[QUOTE=yawmwen;40647866]if we know more about the nature of prime numbers, it would probably break our encrypting algorithms. shor's algorithm, for example, will make modern encryption obsolete.[/QUOTE] That's pretty goddamn serious isn't it

[QUOTE=Octocow;40646943]I don't know what any of this means[/QUOTE] Prime numbers have soul mates that are 70 million units apart. This is a step up from having soul mates infinity unit apart.

[QUOTE=Elecbullet;40649037]That's pretty goddamn serious isn't it[/QUOTE] Shor's algorithm only runs on quantum computers - but as soon as those are capable of factorising numbers bigger than [I]15[/I] yeah there are lots of security implications

[QUOTE=BrainDeath;40651516]Shor's algorithm[/QUOTE] Let all Sons of Skyrim know that the creator of Sovngarde is a giant nerd.

[QUOTE=yawmwen;40647884]they take a lot of cpu to find because there is no simple way to do it without quantum computing. it makes encryption easy. you have a public key that is the product of two very large prime numbers, and a secret key that is the two prime factors. you give out the public key and people are able to use it to encrypt a message to you, but no one will be able to decrypt it because they don't have the prime factors, and it would take ages on a classical computer to find the prime factors. [editline]15th May 2013[/editline] how is this wrong guys? that's how rsa works isn't it? [editline]15th May 2013[/editline] [url]http://en.wikipedia.org/wiki/RSA_%28algorithm%29#Key_generation[/url] i'm not a cryptographer so my explanation was pretty basic, but at least this form of encryption relies on prime factorization being difficult.[/QUOTE] I showed this article to my security teacher. He said it has no effect on rsa and here's why : Rsa relies on being unable to find the prime numbers in a multiplication. (it's really hard to do and there is no fast algorithm besides trying everything) The proof in op says nothing about finding these prime numbers, it just says that there are infinitely many prime numbers with a certain property, which is that they're near other ones. There are still plenty of prime numbers that don't have this property. Don't worry about rsa. [editline]15th May 2013[/editline] Besides the vague statement that "we might might learn more about prime numbers" we have no reason whatsoever to say that this finding makes rsa or other encryption algorithms obsolete and easy to crack.

The security of RSA is based on the difficulty of factoring large number not because the primes used in the algorithm are necessarily quite large. You could know all the primes a key generator uses but you can't know the pair that factors it, in fact, it's the whole factorizing deal that makes it so hard to crack. It's not impossible, it just takes an insane amount of calculation time not feasible with classic computers. And the importance of this is precisely just learning more about prime numbers. The more we know about them, the more we can do with them. RSA serves as a perfect example of a real life application of the properties of prime numbers.

This is the vague reason I mentioned. We might learn more about prime numbers, but this particular thing we learned does not influence the crackability of RSA. Whether we might find something in the future is as much speculation as before this publication was made.

[QUOTE=FPtje;40651979]I showed this article to my security teacher. He said it has no effect on rsa and here's why : Rsa relies on being unable to find the prime numbers in a multiplication. (it's really hard to do and there is no fast algorithm besides trying everything) The proof in op says nothing about finding these prime numbers, it just says that there are infinitely many prime numbers with a certain property, which is that they're near other ones. There are still plenty of prime numbers that don't have this property. Don't worry about rsa. [editline]15th May 2013[/editline] Besides the vague statement that "we might might learn more about prime numbers" we have no reason whatsoever to say that this finding makes rsa or other encryption algorithms obsolete and easy to crack.[/QUOTE] i wasn't talking about this specific case. someone asked what the importance of prime numbers and their properties are.