UCLA group discovers massive prime number

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UCLA mathematicians have discovered a 13-million-digit prime number, marking the 46th known Mersenne prime, which qualifies them for a $100,000 prize. This discovery was made using a network of 75 computers running Windows XP, with verification performed by a different system employing an alternative algorithm. The significance of large prime numbers extends beyond mere curiosity, as they play a crucial role in encryption, particularly in public key cryptography, despite the impracticality of using such large primes for everyday encryption needs.

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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!
 
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Math Is Hard said:
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?
 
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Pffft. Chuck norris counted to infinity,....twice. Don't see him boasting.
 
Cyrus said:
Pffft. Chuck norris counted to infinity,....twice. Don't see him boasting.
I've told Chuck a million times not to exaggerate.
 
I found the smallest prime number.
 
jimmysnyder said:
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.
 
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Art said:
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.
 
jimmysnyder said:
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 :biggrin:

I think there should be a '1' is prime campaign.
 
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  • #10
Art said:
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.
 
  • #11
running Windows XP.

Vista was too slow?
 
  • #12
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?
 
  • #13
Ivan Seeking said:
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?
:smile: Maybe it was produced in the LHC.
 
  • #14
Borek said:
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.
 
  • #15
Ivan Seeking said:
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?

:smile:

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?
 
  • #16
I read somewhere that a quantum computer was built that factored the number 15. That was my public key.
 
  • #17
"Now we're looking for the next one, despite the odds."
Oh, that took a LOOOOOOONNNNNGGGGGG time to sink in. GROAN!
 
  • #18
Moonbear said:
:smile:

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.
 
  • #19
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).
 
  • #20
jimmysnyder said:
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.
 
  • #21
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?
 
  • #22
what surprises me is that the seti@home copycat prime number searcher people didn't find it first.
 
  • #23
jimmysnyder said:
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 =)
 
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  • #24
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.
 
  • #25
tribdog said:
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?
 
  • #26
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.
 
  • #27
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...
 
  • #28
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...
 
  • #29
WarPhalange said:
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.
 
  • #30
Are you alluding to schemes to predict primes?
 

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