Largest Prime Number Found!

[jordan]

I wasn't saying it was. I was just trying to explain what YT was saying and in the process, make sure I understood it myself (YT, you're still welcome to correct me if I explained your theory wrong). I know there are an infinte number of primes. It's my favorite proof because it's so simple yet has great implications. Sorry for any confusion.

[aommaster]

Its ok. I understood YT's theory very well (one of the few things that I understand!), but, remember, you have have x^infinity, you can't write it out, and it makes no sense as infinity is not a number!

[Dave]

I wasn't saying it was. I was just trying to explain what YT was saying and in the process, make sure I understood it myself (YT, you're still welcome to correct me if I explained your theory wrong). I know there are an infinte number of primes. It's my favorite proof because it's so simple yet has great implications. Sorry for any confusion.

 

Yes, the proof is quite elegant and nice. It's just proving the Fundamental Theory of Arithmatic that's the hard bit; the infinite number of primes is almost a Corollary of that.

[jordan]

I'm not familiar with the Fundamental Theory of Arithmatic. Can you explain? It might just be one of those cases where I didn't recongize something by it's name. I find the name pretty trivial and tend to forget them easily.

[admiral_ju00]

I'm not sure I get this, but what exactly does this signify?

Ok, so now there is a number made up of 2 or 6(or whatever)mil chars, but where and how and why would you employ it?

[aommaster]

Are you taking about pi or a prime number?

[admiral_ju00]

the prime number

[aommaster]

Prime numbers are mainly used for encryption. For example' date=' in networking (e.g. Internet) data stream encryption. Large prime number are difficult to be cracked,because calculating them are impractical even for cutting edge CPUs.

As I know, governments will pay lots of money for a large prime number .

By the way, some of the large prime numbers can be copyrighted, which means using them could be illegal......[/quote']

 

That's it

[admiral_ju00]

thanks.

[aommaster]

ur welcome

 

If you are wondering what pi can be used for, I think it could be used in places like nasa, where they try to calculate the area where rockets should be launched and speed of planets and other tuff. The more digits, the more accurate the calculation are! But, I don't think they would use it to that level of accuracy! The best reason I would think that would keep people going would be to see if there ever was an end of pi!

[Dave]

I'm not familiar with the Fundamental Theory of Arithmatic. Can you explain? It might just be one of those cases where I didn't recongize something by it's name. I find the name pretty trivial and tend to forget them easily.

 

You definately know it; FTA states that any natural number can be written as a product of primes.

[jordan]

That's kind of important is proving there are infinite primes. I have heard of it. Do you know the proof?

[Martin]

That's kind of important is proving there are infinite primes. I have heard of it. Do you know the proof?

 

suppose it were not true

then there is a natural number that you cant write as a product of primes

pick the smallest such number

 

 

either it is prime (in which case it is writable as a product of primes namely itself)

 

or it is not prime (in which case it can be factored into two smaller numbers which can each, by assumption, be factored into products of primes)

[jordan]

It looks like you were stating the proof that there are an infinite number of primes. I was looking for the proof of the FTA. Thanks for any and all help.

[Martin]

... FTA states that any natural number can be written as a product of primes.

 

sorry for the misunderstanding, I was just offering a proof for what Dave said, namely any number is a product of primes

 

please tell me if you see a mistake

 

I think what I said proves that any number can be written as a product of primes (because if not then pick the smallest number that cant be...etc)

 

 

would you like a proof that there are infinitely many prime numbers?

[Martin]

I think it must be very easy to see that there cannot be only a finite number of primes because if there were

 

then one could multiply them all together and add one to it.

 

then one would have a number that is not divisible by any of them

 

It would be that monstrosity which we know is not! It would be a number which cannot be written as a product of primes.

 

 

just like if 2,3,5, and 7 were the only primes one could multiply them

all together to get 210

and then add one to it to get 211

 

and that would not be divisible by 2,3,5, or 7

 

because when you divided by any of them you always get the remainder of one.

[jordan]

Ok, so that was a proof for the FTA you had before. I wasn't sure how it worked then. It looked very similar to the proof that there are an infinite number of primes, but I understand what you were saying. Thanks.

[cosine]

Finding pi to the x trillonth digit is useless' date=' you say?

 

Why?

 

My goal in life is to prove that pi does indeed end! I just have to remember how you get pi in the first place lol.[/quote']

 

Thats easy, just change what dimension you're considering!

[Mobius]

My goodness Martin.....

 

this proof of infinite prime numbers was done by Euclid many a moon ago....

 

with regards to the important of large prime numbers and their importance....

just ask a computer security expert.....

[Anjruu]

There is a point in calculating the digits of pi. It is to look for patterns in pi. I'm not sure what the point of THAT is, but it would be interesting. The Chudnovsky brothers have done a lot with this, but so far they havn't found anything.