New Largest Known Prime Number: 2^57,885,161-1

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New Largest Known Prime Number: 2^57,885,161-1

Posted by timothy on Tuesday February 5, 2013 @05:07AM from the sorry-won't-fit-on-vanity-plate dept.

An anonymous reader writes with news from Mersenne.org, home of the Great Internet Mersenne Prime Search: "On January 25th at 23:30:26 UTC, the largest known prime number, 257,885,161-1, was discovered on GIMPS volunteer Curtis Cooper's computer. The new prime number, 2 multiplied by itself 57,885,161 times, less one, has 17,425,170 digits. With 360,000 CPUs peaking at 150 trillion calculations per second, GIMPS — now in its 17th year — is the longest continuously-running global 'grassroots supercomputing' project in Internet history."

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Wrong by Anonymous Coward · 2013-02-05 05:11 · Score: 5, Informative

Actually it would be 2 multiplied by itself 57,885,160 times, minus 1.
1. Re:Wrong by chalsall · 2013-02-05 05:55 · Score: 5, Informative
  
  As is well known, there is no direct mathematical benefit from finding these primes.
  It is, however, a very useful "driving problem" to developing new algorithms, software, and distributed computing infrastructure which have wide ranging real-world applications.
  Check out the Mersenne Forum where all types of interesting mathematical, software and computer issues are discussed.
2. Re:Wrong by Anonymous Coward · 2013-02-05 05:59 · Score: 5, Insightful
  
  Your first question: "What has it added to the study of prime numbers?", I'm not sure but...
  Your second question: "What use is that? (the study of prime numbers)"
  Well... Nearly all modern public key cryptography (SSL / TLS / SSH etc.) is based on the asymmetry in time between the multiplication of two prime numbers (very fast operation) and the factorization of the result back into these two primes (very very slow: the goal being to make so slow that it become impractical to do).
  Actually, it's "worse" than that: the "proof" that most modern PKCS crypto works is: "It's hard to find the (prime) factors of the product of two primes".
  In other words: the study of prime numbers is one of the most important area of mathematics when it comes to computer security.
3. Re:Wrong by Charliemopps · 2013-02-05 06:11 · Score: 4, Informative
  
  http://primes.utm.edu/notes/faq/why.html
4. Re:Wrong by Anonymous Coward · 2013-02-05 06:35 · Score: 5, Funny
  
  I can't speak for other people, but I often use (2^57,885,161)-1 in casual conversation.
5. Re:Wrong by cryptizard · 2013-02-05 08:35 · Score: 4, Interesting
  
  Actually, it's "worse" than that: the "proof" that most modern PKCS crypto works is: "It's hard to find the (prime) factors of the product of two primes".
  Small correction, there is actually no proof that RSA reduces to factoring. It is true that if you can factor you can break RSA, but you may also be able to break RSA without factoring. http://en.wikipedia.org/wiki/RSA_problem
6. Re:Wrong by jc42 · 2013-02-05 12:53 · Score: 4, Insightful
  
  Do I believe Wikipedia? Or do I believe Donald Knuth?
  Why should you believe either? One of the basic (meta-)principles of mathematics is that you don't have to take anyone's word for something. You can check out their claim yourself, using existing reference material and your own mind. This isn't facetious; mathematical and scientific results have occasionally been shown to be erroneous.
  If you are unwilling to do these things, you're abandoning your (and your children's) future to those who are willing to do them (or to pay others to do them ;-). The dominant power and wealth in the human society now belongs to those who can handle technology. If you demand belief rather than understanding, you are handing control over to those willing to gain the understanding.
  If you can't appreciate the aesthetic justifications for learning about math and science, you certain must be aware of the history of successes and improvements in our world by their practitioners. Few of us would like to go back to stone-age hunter-gatherer societies. It's the experimenters and reasoners that got us past that stage.
  
  --
  Those who do study history are doomed to stand helplessly by while everyone else repeats it.
Re:Uhhh... by SuricouRaven · 2013-02-05 05:15 · Score: 5, Informative

2^4-1 = 16-1 = 15.
5 * 3 = 15.
Go read it again.
Re:Uhhh... by fredprado · 2013-02-05 05:24 · Score: 4, Informative

Mathematics does deal with a lot of "disputed" definitions. Mathematics deal even with a lot of "disputed" logic and "disputed" interpretations. Read about the axiom of choice, set Theory in general, Constructivism (mathematics) and Finitism and you will understand that things get quite more complicated than you thought.
A Little More Perfection by 14erCleaner · 2013-02-05 05:28 · Score: 5, Informative

Since the only known perfect numbers are derived from Mersenne Primes, this means there are also now 48 known perfect numbers. Interestingly, this property of Mersenne Primes was discovered by Euclid about 2000 years before Mersenne was born (time machine, anyone?). Finding a non-Mersenne perfect number would be a huge accomplishment.

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Re:Why 2^n-1 by godrik · 2013-02-05 05:28 · Score: 4, Informative

number of the form 2^n-1 are Mersenne numbers which are much more likely to be prime than a randomly chosen odd number. Also, we have "simple" test for these number to weed out many Mersenne numbers that are not prime. Once you have a Mersenne number that passed the "simple" primality test, there is a good chance that it will really be a prime number.
Re:Uhhh... by amicusNYCL · 2013-02-05 05:34 · Score: 5, Funny

Hey, has anyone told you that your post is wrong yet?

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"Our two-party system is like a bowl of shit looking at itself in a mirror." - Lewis Black
Re:Uhhh... by NoNonAlphaCharsHere · 2013-02-05 05:36 · Score: 4, Funny

Mathematics may not deal in disputed definitions, but Wikipedia certainly does.
Re:Uhhh... by Anonymous Coward · 2013-02-05 05:38 · Score: 5, Insightful

111 1111 1111 == 2047 == 23 * 89
Funny how many assertions here that number disproves
Re:Why 2^n-1 by Anonymous Coward · 2013-02-05 05:41 · Score: 4, Informative

There is a very fast primality test for Mersenne numbers, the Lucas–Lehmer primality test.
2^n+1 is prime only if it's a Fermat prime, n=2^k. None of these are known to be prime for k>4, and there probably aren't any more, whereas there are probably infinitely many Mersenne primes.
Number of Digits by necro81 · 2013-02-05 05:47 · Score: 5, Interesting

The new prime number, 2 multiplied by itself 57,885,161 times, less one, has 17,425,170 digits
"There are 10 kinds of people in the world. Those who understand binary, and those that don't."

This new number is 2^57,885,161 - 1, so naturally it has 57,885,161 digits, all of them 1. A simpler example: 2^5 - 1 is a Mersenne prime. Written in binary it's 100000 - 1 = 11111.

Oh! You meant that it has 17,425,170 decimal digits. Booooooooring!
Re:They would have more primes to choose from ... by dwillmore · 2013-02-05 05:51 · Score: 4, Interesting

Yes. The LL test only works on Mersenne numbers--numbers of the form 2^p-1 where p is prime. The LL test is not statistical. It can determine if a given mersenne number is prime or not without any doubt.
To protect against errors, GIMPS (Great Internet Mersenne Prime Search) uses a variety of double checks to ensure no number if mistested. Any number that passes the LL test is double (and sometimes triple checked) to verify that there wasn't a hardware or software error that caused a false positive. I had the honor of performing the double check of a record Mersenne prime some time ago.
Re:CPUs? why not GPUs? by chalsall · 2013-02-05 06:11 · Score: 5, Informative

Yes. And both are used for GIMPS.
See the Mersenne Forum's GPU Computing sub-forum for details.
There are, however, many more CPUs than GPUs out there, so most of the work is still done by CPUs. Two different GPUs using different software (CUDALucas) were used to confirm that 2^57,885,161-1 was prime, in addition to two other CPUs (one using different software than the GIMPS standard Prime95/mprime).
Re:Uhhh... by sgunhouse · 2013-02-05 07:12 · Score: 4, Interesting

If the exponent is not prime, then the number will not be prime.
I don't do HTML, I'll use the symbol ^ for exponent (I don't do C either). Let's suppose c = a*b, then 2^c - 1 is divisible by both 2^a - 1 and 2^b - 1. (That's true with x instead of 2, the difference being 2^1 - 1 is 1 which is not prime.) Whether the definition requires primality or not, mathematics dictates that the exponent must be prime.