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2013-06-04 02:48:26

30 votes, rating 5.6

30 votes, rating 5.6

Twin Prime Conjecture

For those of you interested in math, you will know that professor Zhang proved that there are infinite pairs of primes separated by at most 70 million, several weeks ago. He also included in his work the details for how to reduce this number, and since then someone else has indeed followed that work through and proved that the separation is at most some 63 million.

I, following a rather different method, have just finished writing up a formal proof of the entire Twin Prime Conjecture. I will be presenting to my local University within a week, and hopefully publishing the proof shortly after that. My proof also provides the method to prove an infinite class of pairs of primes that are separated by even numbers, including any multiple of 200, which includes the 70 million proved by Zhang.

My work also shows that there can be significant work done on identifying not only that such pairs exist, but defining limits on how many such pairs must exist in relatively small intervals - this method can then further be expanded into primes, not just twin primes, and could help with predicting primes in general, although I don't think it will actually lead to predicting individual primes, but it might lead to methods that are easier to predict individual primes.

I, following a rather different method, have just finished writing up a formal proof of the entire Twin Prime Conjecture. I will be presenting to my local University within a week, and hopefully publishing the proof shortly after that. My proof also provides the method to prove an infinite class of pairs of primes that are separated by even numbers, including any multiple of 200, which includes the 70 million proved by Zhang.

My work also shows that there can be significant work done on identifying not only that such pairs exist, but defining limits on how many such pairs must exist in relatively small intervals - this method can then further be expanded into primes, not just twin primes, and could help with predicting primes in general, although I don't think it will actually lead to predicting individual primes, but it might lead to methods that are easier to predict individual primes.

Comments

Posted by Lorebass on 2013-06-04 03:00:50

Did you just throw complex math at us?

I wasn't aware anyone here could count higher than 16.

Go for it tho!

I wasn't aware anyone here could count higher than 16.

Go for it tho!

Posted by Nelphine on 2013-06-04 03:11:23

No, not complex. Complex numbers are for chumps. (Ok not really, but I think they have no business in prime number theory.)

Posted by xnoelx on 2013-06-04 03:11:40

It's mathS, goshdurnit!

That aside, impressive...

That aside, impressive...

Posted by huff on 2013-06-04 03:16:51

Does this help us solve our min-max problem?

Posted by truckerpunk on 2013-06-04 04:22:42

Yay.. science nerds! Rated 6!

Posted by Jeffro on 2013-06-04 04:31:01

someone tell me again that 'i' is a number...

go on... try

go on... try

Posted by Nelphine on 2013-06-04 04:50:23

i is NOT a number.

i is an imaginary number.

it acts like a number that was equivalent to the square root of -1 would act, if that number could exist. since that number can't actually exist, i, which is not a number, was created, to have properties similar to such an imaginary number.

if you have no need of the square root of -1, then not only does i not exist as a number, it also doesn't exist as a useful concept.

i is an imaginary number.

it acts like a number that was equivalent to the square root of -1 would act, if that number could exist. since that number can't actually exist, i, which is not a number, was created, to have properties similar to such an imaginary number.

if you have no need of the square root of -1, then not only does i not exist as a number, it also doesn't exist as a useful concept.

Posted by baelnic on 2013-06-04 05:51:26

I feel like this blog should only be rated in prime numbers although I rated it 1 for purity.

Posted by Jeffro on 2013-06-04 06:59:37

Woo-dang, dog...

http://s3-ec.buzzfed.com/static/enhanced/terminal05/2012/8/14/22/enhanced-buzz-14667-1344996501-9.jpg

http://s3-ec.buzzfed.com/static/enhanced/terminal05/2012/8/14/22/enhanced-buzz-14667-1344996501-9.jpg

Posted by Overhamsteren on 2013-06-04 07:23:26

Privateer Press is releasing a new army for Warmachine these days, it's called Convergence of Cyriss and its fluff is based on maths, often prime numbers!!!!!!

Posted by Overhamsteren on 2013-06-04 07:24:52

also

i is not a number! i is a free man!

i is not a number! i is a free man!

Posted by Meltyman on 2013-06-04 08:17:10

I can count to potato

Posted by dfunkateer on 2013-06-04 08:20:12

My brain hurts

Posted by the_Sage on 2013-06-04 09:34:37

lol@overhamsteren.

Congratulations Nelphine, this sounds like a major accomplishment in mathematics.

Can you tell me whether/how this might affect the field of cryptanalysis?

Congratulations Nelphine, this sounds like a major accomplishment in mathematics.

Can you tell me whether/how this might affect the field of cryptanalysis?

Posted by jamesfarrell129 on 2013-06-04 10:03:02

Can I rate this pi?

Posted by eldritchfox on 2013-06-04 10:07:39

Not Optimus Prime then??? Damn it.

Posted by Badoek on 2013-06-04 10:23:24

I fail to see how this helps our problems with the RNG. Explain!

Posted by Nelphine on 2013-06-04 10:25:22

@The_Sage:

It depends on whether I can actually work out how to isolate primes (or small numbers of primes in small intervals). If I could do that, then given a certain set of parameters to define the interval (such as the information given in internet security encryption), and my methods, you could quickly check all the numbers in the interval to determine which ones were prime.

If everything goes perfectly (har har, not in the world of primes), this would mean determining what prime numbers are used in any given internet data exchange could actually become a reasonable task, which would have drastic consequences on most security measures currently used for online communication.

It depends on whether I can actually work out how to isolate primes (or small numbers of primes in small intervals). If I could do that, then given a certain set of parameters to define the interval (such as the information given in internet security encryption), and my methods, you could quickly check all the numbers in the interval to determine which ones were prime.

If everything goes perfectly (har har, not in the world of primes), this would mean determining what prime numbers are used in any given internet data exchange could actually become a reasonable task, which would have drastic consequences on most security measures currently used for online communication.

Posted by Nelphine on 2013-06-04 10:26:59

@Badoek:

At the extreme best case scenario, this could be used to determine the generating formula for the RNG, and thus allow you to predict it in it's entirety.

From a practical viewpoint, I doubt that would happen in the near future though. My proof simply isn't in depth enough to actually threaten internet communication - it merely points out a method that might be used to do so.

At the extreme best case scenario, this could be used to determine the generating formula for the RNG, and thus allow you to predict it in it's entirety.

From a practical viewpoint, I doubt that would happen in the near future though. My proof simply isn't in depth enough to actually threaten internet communication - it merely points out a method that might be used to do so.

Posted by PurpleChest on 2013-06-04 12:27:44

Well, cool.

Go you.

The range and type of nerd on FUMBBL never ceases to amaze me.

Go you.

The range and type of nerd on FUMBBL never ceases to amaze me.

Posted by billiebob on 2013-06-04 12:38:12

Awesome.

Posted by latulike on 2013-06-04 13:04:30

Imo, good maths are real life useful maths. So any maths you've learned as a kid/teenager (or even adult )that helps you build things, win at bloodbowl or budget your finances is good math to me.

Now please explain to me where prime numbers are useful?

Now please explain to me where prime numbers are useful?

Posted by Rabe on 2013-06-04 13:43:33

Awesome blog entry, some comments alone made me love in a way that got me out of my sub-prime mood. :-D

I don't really get what you're telling us (I might do with some further explanation), but still I like to congratulate you on your success. :-)

I don't really get what you're telling us (I might do with some further explanation), but still I like to congratulate you on your success. :-)

Posted by Rabe on 2013-06-04 13:44:35

"Posted by Overhamsteren on 2013-06-04 07:24:52

also

i is not a number! i is a free man!"

This in particular made my day. Thanks, OH! :-D

also

i is not a number! i is a free man!"

This in particular made my day. Thanks, OH! :-D

Posted by oryx on 2013-06-04 14:37:49

Love it all!

Posted by Hitonagashi on 2013-06-04 14:45:30

As an amateur number theorist, colour me impressed. Be interesting to see how that goes!

Posted by Nelphine on 2013-06-04 17:18:33

@Iatulike:

Prime numbers are used in virtually all online communication security.

If someone can determine a way to easily predict them, most security on the internet would be destoyed, and something else would have to be found - given how good people are at cracking encryption (which is how we keep internet communication secure), it is possible it would take a long time to find a system secure enough to actually call secure again, if we couldn't use prime numbers.

My proof is a step towards predicting all prime numbers, and potentially a major step, since the TPC has been around for over 2000 years without anyone being able to solve it.

For examples of what kind of security I am talking about, consider online banking, password protection, or the ability to literally pick open the RNG used on this website.

While Prime Numbers are not generally used for day to day life by most people, they are certainly used in the day to day life of almost everyone.

Prime numbers are used in virtually all online communication security.

If someone can determine a way to easily predict them, most security on the internet would be destoyed, and something else would have to be found - given how good people are at cracking encryption (which is how we keep internet communication secure), it is possible it would take a long time to find a system secure enough to actually call secure again, if we couldn't use prime numbers.

My proof is a step towards predicting all prime numbers, and potentially a major step, since the TPC has been around for over 2000 years without anyone being able to solve it.

For examples of what kind of security I am talking about, consider online banking, password protection, or the ability to literally pick open the RNG used on this website.

While Prime Numbers are not generally used for day to day life by most people, they are certainly used in the day to day life of almost everyone.

Posted by keggiemckill on 2013-06-04 17:42:55

Where will we be able to find your "proof?" I would be interested in reading it. It above my pay grade, but I find that stuff interesting.

Posted by keggiemckill on 2013-06-04 17:49:54

http://en.wikipedia.org/wiki/Twin_prime

Posted by dode74 on 2013-06-04 18:56:52

Why are you telling people? Complete the theorem, steal a little money from everyone and then live the good life! :D

Posted by garyt1 on 2013-06-04 19:08:36

Now I see why you love the stats. Impressive looking stuff.

Though essentially you are telling us that this work is progressing towards endangering our online (and probably financial) existences! :-O

Though essentially you are telling us that this work is progressing towards endangering our online (and probably financial) existences! :-O

Posted by Christer on 2013-06-04 20:46:58

Just because cryptography is something I find interesting, I'll state that even if we managed to come up with a system that can factor large prime numbers instantly, it wouldn't be the end of encryption. Effectively, there are two major approaches in use when it comes to encrypted web traffic:

1. Asymmetric cryptography, which is based on prime numbers. This is slow and normally only used to encrypt and decrypt a random "session key", which is used to encrypt the bulk of the data being transferred.

2. Symmetric cryptography (mostly block and stream ciphers), which does not rely on prime numbers, but uses other technology (s-boxes being the core, which essentially scramble bits of data)

Now, if prime factorisation would become trivial the first type of crypto would be rendered useless. This would be bad in the short term until major components would switch to other technologies. One of the major alternative approaches is called "Elliptic Curve Cryptography" which could well be used to replace the asymmetric crypto. ECC is very well known and widely used technology.

Basically, it wouldn't be the end of the world to have prime factorisation made trivial.

1. Asymmetric cryptography, which is based on prime numbers. This is slow and normally only used to encrypt and decrypt a random "session key", which is used to encrypt the bulk of the data being transferred.

2. Symmetric cryptography (mostly block and stream ciphers), which does not rely on prime numbers, but uses other technology (s-boxes being the core, which essentially scramble bits of data)

Now, if prime factorisation would become trivial the first type of crypto would be rendered useless. This would be bad in the short term until major components would switch to other technologies. One of the major alternative approaches is called "Elliptic Curve Cryptography" which could well be used to replace the asymmetric crypto. ECC is very well known and widely used technology.

Basically, it wouldn't be the end of the world to have prime factorisation made trivial.

Posted by Nelphine on 2013-06-04 21:43:38

@Christer:

First, I also don't think I would be making prime factorization trivial any time soon. This is just a step towards it.

Second, I was under the (probably mistaken) impression that there were other problems with using ECC for every day communication, and so while it certainly works, it wouldn't work as well.

First, I also don't think I would be making prime factorization trivial any time soon. This is just a step towards it.

Second, I was under the (probably mistaken) impression that there were other problems with using ECC for every day communication, and so while it certainly works, it wouldn't work as well.

Posted by JackassRampant on 2013-06-05 04:00:11

I wanted to rate this one a 7. 6 is just too perfect, you know?

Posted by uuni on 2013-06-05 19:49:06

@Nelphine: Didn't Riemann's Zeta-function tie complex numbers and prime numbers together in some way?

@Christer: Is prime factorisation NP-complete and was there method to translate other NP-complete problems into it? Wouldn't that also affect elliptics?

@Christer: Is prime factorisation NP-complete and was there method to translate other NP-complete problems into it? Wouldn't that also affect elliptics?

Posted by Nelphine on 2013-06-06 00:50:27

@uuni: Of course complex numbers and prime numbers are linked. I just think that's silly, and my work goes in a completely different direction, and has some surprisingly detailed results.