UCLA group discovers massive prime number

[Math Is Hard]

http://www.msnbc.msn.com/id/26914730/from/ET/

LOS ANGELES - Mathematicians at UCLA have discovered a 13-million-digit prime number, a long-sought milestone that makes them eligible for a $100,000 prize.

The group found the 46th known Mersenne prime last month on a network of 75 computers running Windows XP. The number was verified by a different computer system running a different algorithm.

"We're delighted," said UCLA's Edson Smith, the leader of the effort. "Now we're looking for the next one, despite the odds."

Go Bruins!

 

[Art]

http://www.msnbc.msn.com/id/26914730/from/ET/Go Bruins!

What do they use these large prime numbers for? I think I heard one time it was something to do with encryption but if so how does it work? Or is it just for fun?

Edit - I looked it up and it seems encryption is based on the product of 2 large primes (public key) and the primes themselves (private key) but seeing as how 128 bit encryption already yields 3,835,341,275,459,350,000,000,000,000,000,000,000 different prime numbers which would take a computer 121,617,874,031,562,000 years to crack why bother looking for bigger ones or do primes have other uses?

 

[Cyrus]

Pffft. Chuck norris counted to infinity,....twice. Don't see him boasting.

 

[Art]

Pffft. Chuck norris counted to infinity,....twice. Don't see him boasting.

I've told Chuck a million times not to exaggerate.

 

[Jimmy Snyder]

I found the smallest prime number.

 

[Art]

I found the smallest prime number.

Speaking of which why isn't '1' a prime number any more? It used to be. As all other non-prime numbers except '1' are composite numbers it seems unfair to cast the number '1' out into no-man's land.

 

[Jimmy Snyder]

Speaking of which why isn't '1' a prime number any more? It used to be.

You can define prime number as you wish. However, if you define it so that 1 is prime, then you lose the unique factorization theorem among others.

 

[Art]

You can define prime number as you wish. However, if you define it so that 1 is prime, then you lose the unique factorization theorem among others.

Hey somebody has to stick up for the little guys

I think there should be a '1' is prime campaign.

 

[Borek]

https://www.physicsforums.com/showthread.php?t=254451

 

[Borek]

Edit - I looked it up and it seems encryption is based on the product of 2 large primes (public key) and the primes themselves (private key) but seeing as how 128 bit encryption already yields 3,835,341,275,459,350,000,000,000,000,000,000,000 different prime numbers which would take a computer 121,617,874,031,562,000 years to crack why bother looking for bigger ones or do primes have other uses?

I don't have any reference at hand, but I think this information must be outdated. 512 bits key can be breaken in a reasonable time - it was done for the first time not later than in 2000.

 

[LowlyPion]

running Windows XP.

Vista was too slow?

 

[Ivan Seeking]

To find very large prime numbers is impressive, but to find one so large that it has mass is really astounding!

Where did they find it?

 

[Art]

To find very large prime numbers is impressive, but to find one so large that it has mass is really astounding!

Where did they find it?

Maybe it was produced in the LHC.

 

[Art]

I don't have any reference at hand, but I think this information must be outdated. 512 bits key can be breaken in a reasonable time - it was done for the first time not later than in 2000.

Drat, Pipped at the post! I only had 121,617,874,031,561,999 years left in my project to be the first to break it.

 

[Moonbear]

To find very large prime numbers is impressive, but to find one so large that it has mass is really astounding!

Where did they find it?

I'm also wondering "why" as well. Is there a useful reason to need to know it, or is it just a weird hobby that math geeks have?

 

[Jimmy Snyder]

I read somewhere that a quantum computer was built that factored the number 15. That was my public key.

 

[Moonbear]

"Now we're looking for the next one, despite the odds."

Oh, that took a LOOOOOOONNNNNGGGGGG time to sink in. GROAN!

 

[Art]

I'm also wondering "why" as well. Is there a useful reason to need to know it, or is it just a weird hobby that math geeks have?

Let's face, it with 13 million figures they could tell us anything. It's not as if we're going to go away and check it.

 

[Math Jeans]

I think that we should move on from prime numbers to something more interesting.

Maybe morphing a code with a similar concept to Arnold's Cat Map. That would be fun. (unless they already have done that in which case I just feel stupid).

 

[Ivan Seeking]

I read somewhere that a quantum computer was built that factored the number 15. That was my public key.

Yes, but it had the answer before it started the calculation.

 

[tribdog]

Why would they want to find big primes? Are you kidding? Ask Hillary why he climbs mountains. Ask Phelps why he tries to swim faster. Where is your sense of exploration and discovery?

 

[tribdog]

what surprises me is that the seti@home copycat prime number searcher people didn't find it first.

 

[Howers]

You can define prime number as you wish. However, if you define it so that 1 is prime, then you lose the unique factorization theorem among others.

No you don't, every number can be factored by one.

I don't know why 1 isn't prime, it most definitely should be. My guess is that it makes the definition easier to maintain: a prime number is a number that has two distinct factors.

EDIT: Hmmm... never mind, you lose uniqueness. Very good point =)

 

[tribdog]

I'm not a mathematician but here's what I was told. 1 is the only natural number whose reciprocal is also a natural number therefore it is called unity and unity is never prime. Also a number evenly divided by a prime number reveals certain properties of that number, but a number divided by 1 reveals nothing.

 

[Howers]

I'm not a mathematician but here's what I was told. 1 is the only natural number whose reciprocal is also a natural number therefore it is called unity and unity is never prime. Also a number evenly divided by a prime number reveals certain properties of that number, but a number divided by 1 reveals nothing.

What property does a number being divisible by 7 reveal? Besides the obvious...

Why can't unity be prime? Its an arbitrary definition. Should 1 not be odd either?

 

[tribdog]

isn't the obvious enough? not all numbers can be divided by 7 so it gets put into a rather selective category doesn't it? I don't know the exact numbers but something like only 1 in 20 numbers can be divided by 7.

 

[WarPhalange]

Isn't it as simple as having some odd number X, and seeing if it is divisible by any previous odd numbers up to X/2, rounded up or down or whatever? You'd eventually find all of them, if you waited long enough...

 

[tribdog]

BTW my own personal opinion as to why 1 isn't prime is because when they went to print out the list of primes Fibonacci stole the last die of a 1 because he wanted to start his list 1,1,2...

 

[tribdog]

Isn't it as simple as having some odd number X, and seeing if it is divisible by any previous odd numbers up to X/2, rounded up or down or whatever? You'd eventually find all of them, if you waited long enough...

you know how big this number is? it takes a long long long long long time to do that. And who says there is an "all of them" there might be an infinite number of primes.

 

[Ivan Seeking]

Are you alluding to schemes to predict primes?

 

[Howers]

you know how big this number is? it takes a long long long long long time to do that. And who says there is an "all of them" there might be an infinite number of primes.

There is an infinite number, that's what Euclids theorem says isn't it?

I think the best reason is jimmysnyders: you lose unique facotrization, as 1 can appear as many times as one pleases.

 

[jhicks]

What do they use these large prime numbers for? I think I heard one time it was something to do with encryption but if so how does it work? Or is it just for fun?

Probably answered by now, but as far as I know prime numbers themselves are useless for encryption. The RSA algorithm makes use of numbers with 2 large factors, however. Realistically though, we passed the point a decade ago of finding numbers suitable for everyday encryption. 13 million digits is astoundingly large to be of any practical use.

And Howers is right; Euclid proved forever ago that there are an infinite number of prime numbers with only a couple of short statements.

 

[Borek]

I don't know the exact numbers but something like only 1 in 20 numbers can be divided by 7.

About three times that, as long as we are in the realm of not exact numbers.

 

[vanesch]

This is an amazing discovery. Until now, I thought prime numbers were massless :shy:

edit: oops, ivan made this joke already...

 

[vanesch]

isn't the obvious enough? not all numbers can be divided by 7 so it gets put into a rather selective category doesn't it? I don't know the exact numbers but something like only 1 in 20 numbers can be divided by 7.

Bwahahaha ! I'd think that about 1 number in 7 can be divided by 7

 

[schroder]

isn't the obvious enough? not all numbers can be divided by 7 so it gets put into a rather selective category doesn't it? I don't know the exact numbers but something like only 1 in 20 numbers can be divided by 7.

Isn’t every seventh number (starting from seven) divisible by seven? And if you take the product of all the prime numbers, up to and including the so-called “largest prime” and add one to that, this new number is either a prime or it contains a prime larger than the previous largest. The number of primes is therefore infinite.

 

[Howers]

Isn’t every seventh number (starting from seven) divisible by seven? And if you take the product of all the prime numbers, up to and including the so-called “largest prime” and add one to that, this new number is either a prime or it contains a prime larger than the previous largest. The number of primes is therefore infinite.

way to steal vanesch's joke. i award you -7 points.

 

[Art]

Bwahahaha ! I'd think that about 1 number in 7 can be divided by 7

Looks like some folk here haven't done their 7 * table yet.

 

[tribdog]

way to steal vanesch's joke. i award you -7 points.

vanesch's joke? VANESCH'S JOKE?

 

[Howers]

To be honest, I came here only for the post count.

 

[Art]

Isn’t every seventh number (starting from seven) divisible by seven? And if you take the product of all the prime numbers, up to and including the so-called “largest prime” and add one to that, this new number is either a prime or it contains a prime larger than the previous largest. The number of primes is therefore infinite.

So Euclid says anyway... but then what does he know

 

[Borek]

To be honest, I came here only for the post count.

Try harder, posts in GD don't count.

 

[tribdog]

To be honest, I came here only for the post count.

If posts in here counted I'd have several thousand. If they'd let me out of here I'd thousands too.

 

[Jimmy Snyder]

About three times that, as long as we are in the realm of not exact numbers.

Is this the joke? If so, Borek should get the credit. I thought it was a good one.

 

[Ivan Seeking]

This is an amazing discovery. Until now, I thought prime numbers were massless :shy:

edit: oops, ivan made this joke already...

That's okay, some jokes are worth telling twice.

I thought only Catholic numbers have mass.

 

[Monique]

Why don't they use the computer power for something useful? Calculating massive prime numbers was used to test the computational power of computers, I think they have gone far enough.

 

[kingdomof]

Monique, ever hear of Folding@Home?

There are plenty similar projects, don't worry, heh.

 

[Howers]

Is this the joke? If so, Borek should get the credit. I thought it was a good one.

Haha, yeah. I totally missed that. That non-exact numbers thing threw me off.

Try harder, posts in GD don't count.

Argh. You've out witted us all.

Maybe I should return to Academic Guidance and tell people what book they need to study linear algebra. That should put me in the 1000s by next week!

 

[Borek]

Is this the joke? If so, Borek should get the credit. I thought it was a good one.

Joke? I was deadly serious.

 

[tribdog]

its a joke when Borek says it, but no one had a problem believing I thought 1 in 20 numbers is divisible by 7? I don't know if I should be offended or if this is just another case of "don't feed the tribdog"