of interest to math nerds and internet business users alike

[plusminus]

http://www.whatpc.co.uk/news/1157891

edit: I suppose this includes everyone with a gold account here, no?

[Walrus]

most people ive met consider me a maths nerd since i got an A in AS level, and i found that quite interesting. i thought the whole prime number thing had been solved ages ago, had no idea people were still puzzling about it.

[Jonspen]

Wha???? What the f*** is this plus???

[plusminus]

Basically prime numbers are numbers which are divisible only by themselves, and 1, without getting a decimal answer. 2 is the only even prime because after that, any even number can be divided by 2. 1 is not a prime because there is only one number that it can be divided by, that being 1.

The prime number series starts 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and goes on from there up to gigantic numbers. It has long been thought that there is possibly some pattern to the prime number series, but never proven. However, the mathmatician mentionned in the article claims he's on the verge of figuring out the pattern.

The thing is, that since it was assumed that if there even was a pattern to the numbers it wouldn't be solved, and so it was a "safe" system to use for encrypting data. (It's like Y2K all over again, in a sense.) A *large* number of cryptography is done based around this assumption, including virtually any encryption done for eCommerce on the internet.

The way it works is because prime numbers were thought to have no pattern, you could choose two of them and then generate an encryption key which would be *very* time-consuming to break. This made data encrypted by the key "safe". However, if the pattern becomes easily identifyable, then the safeness of the system decreases considerably.

For a better explaination on how cryptography works: http://www.math.toronto.edu/007/007-news.html#RSA

[Jeffery]

Originally posted by Walrus
most people ive met consider me a maths nerd since i got an A in AS level, and i found that quite interesting. i thought the whole prime number thing had been solved ages ago, had no idea people were still puzzling about it.

http://rds.yahoo.com/S=2766679/K=student+prime+number/v=2/SID=e/l=WS1/R=1/H=0/IPC=us/SHE=0/*-http://www.cnn.com/2003/TECH/science/12/11/prime.number.ap
You might want to check into this. There is no "end" to prime numbers. There will always be the next higher prime number to be found.

[Walrus]

i know, arent the u.s army offering like 100000 to whoever can find a 10 million digit prime number?

[Glamdring]

Indeed, there is none. I figured that out on my own when I had lots of spare time on my hands. It's complicated, but not too terribly difficult to prove.

Even if the pattern is identified, I seriously doubt the system will ever become a problem. It would require some seriously genius hackers.

[Office_Shredder]

two things about the army offering money for a prime number:
a.) wtf would be the purpose of that?
b.) it wouldn't be that hard to find one, since prime numbers aren't more spaced out over time (unless you count the fact that since 2 and 3 are prime, so 2/3 of 1 through three are prime). A simple algorithm on a computer will give it to you eventually (it'll take a while, but it's worth if for that much money)

[Glamdring]

Yes, they are more spaced out over time. Believe me.

[Office_Shredder]

Ok, I guess I was a bit hasty in stating that they aren't spaced out more over time, what I should have said was:

It's not like prime numbers get spaced out so fast that you'll have to spend forever algorithmically searching for one

[Walrus]

Originally posted by Glamdring
Yes, they are more spaced out over time. Believe me.

what she said



its coz, if you think logically, a higher number can be a multiple of more other numbers.

9 would be a prime number, if not for the fact that 3, a prime number itself, wasnt timesd by 3 to make it (9)
this may seem obvious, but with larger numbers it becomes less aparrent.

17 is a p.n
times that by 3 and u get 51, which would be a prime number (i think) if not for that 17x3.

as you go up the series, more and more of the smaller prime numbers get added to this chain, meaning they get more spaced out.


anyway im going to bed, and i doubt you understand what i said there, coz i find it hard to explain in words

[ArcPaladinZero]

With enough time anything can be hacked. There will always be more security. When it comes down to it, it all depends on who has the time and how much of it they have.

[Office_Shredder]

walrus, I agree with what you're saying, and when I said they don't get more spaced out over time I didn't mean linearly.... it was more of a proportions kind of thing.

[plusminus]

You're right that this probably won't be an immediate problem to people who still want to buy things with their credit card over the internet.

However, so very much of cryptography is based around the principle that it takes extremely long to factor the product of two primes. Proving this hypothesis would not immediately help with the factoring, but it may lead to much easier ways of factoring said numbers, because it provides a basis of a patten.

Interestingly, a whole lot of number theory is based on the assumption that Riemann's hypothesis is true. If it were proven otherwise, that would be an equally big deal.

EDIT: And this is just funny. http://members.surfeu.fi/kklaine/primebear.html

[Tecibbar]

That's a really interesting news. I don't know that theory. How much more information can we know about big primes. Like we will have a more acuate guess of if a number is prime, or we can use a very easy algorithm in linear or square time to derive all primes?

I understand a bit of web-encry, but couldn't people just use other ways to encry information?

[Aro23r]

does anyone here have a picture of, or know the actual formula? I know some upper-level mathematics and would like to see what it looks like.

[plusminus]

This is heavy reading, Aro23r:

http://mathworld.wolfram.com/RiemannHypothesis.html
http://www.math.purdue.edu/~branges/

[Aro23r]

Apparently introductory to AP Calculus AB is not even close to required, although, I do understand some of the symbols :)

[plusminus]

This stuff truly makes my head hurt even trying to grasp what is being discussed in the formula...

There is an interesting page about the guy who has the supposed proof, that makes considerably more sense to me than either of those past two links: http://www.lrb.co.uk/v26/n14/sabb01_.html

[T3km4n]

Math classes suck, but that stuff kind of amazed me in how complicated it is.

[xyxaxyz2]

And I always thought this math theory stuff was pointless....

[plusminus]

Math is the one true universal language.

And if you don't buy that, well then... perhaps one day you will be on a train headed for boston, wondering when the train that left 2 hours before you in the other direction will pass you, cursing yourself the whole time. ;)

[Warcow]

That crap reminds me of the divine proportion, or so its called, if anyone has read the davinchi code they will know what i'm talking about, aparently there about 784978273480 proportions in nature that always end up being the same, Kind of makes you wonder doesnt it?

[Glamdring]

My calculus and physics teachers each mentioned the Riemann Hypothesis a few times... They only ever brought it up to say "see, if you're insane enough to continue in math long enough, you'll eventually understand this."

[Walrus]

Walruses 2nd Theory (yes there was a 1st, its in CAU under the subliminal message ward thread)

x is directly proportional to y

where
x = "height" of prime number in the entire number sequence
y = length of time the prime number shitting bear has been on for.


this is the guiding principle from which all these other theorums have arisen

[Bottle]

To prove that there is no largest prime number.

Initially assume that there is a largest prime number, A.

Then form n = product of all primes + 1, ie. n = (2 x 3 x 5 x 7 x 11.....x A) + 1

Clearly, this number is not divisible by any of the primes in the collection, because in each case it leaves a remainer 1. Therefore, n is also prime. However, n is also greater than A, so our initial assumption is contradicted.

Therefore, the number of prime numbers is infinite.

[xyxaxyz2]

Originally posted by plusminus
Math is the one true universal language.

Considering that there seem to be only about 5 people who can understand this stuff. :cool:

[Office_Shredder]

Originally posted by Bottle
To prove that there is no largest prime number.

Initially assume that there is a largest prime number, A.

Then form n = product of all primes + 1, ie. n = 2 x 3 x 5 x 7 x 11.....x (A+1)

Clearly, this number is not divisible by any of the primes in the collection, because in each case it leaves a remainer 1. Therefore, n is also prime. However, n is also greater than A, so our initial assumption is contradicted.

Therefore, the number of prime numbers is infinite.

You made a slight mistake... you put
n = 2 x 3 x 5 x 7 x 11.....x (A+1)
when it should be
n = (2 x 3 x 5 x 7 x 11.....x A) +1

Otherwise you're multiplying your prime numbers by a composite number (unless you're suggesting the whole proof falls apart because A+1 is prime :))

[abyaly]

It's ironic when someone corrects someone on a detail, but the correction also has a detail wrong :)

[Office_Shredder]

what detail is that?

[Bottle]

Oops. :o

That'll teach me to do complex maths and play TAO at the same time. :)

[Jeffery]

Originally posted by abyaly
It's ironic when someone corrects someone on a detail, but the correction also has a detail wrong :)

Yeah, what detail is that. He gave the correct correction of the product of all prime +1.

[Office_Shredder]

That's right bottle..... hang your head in shame :p