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 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.
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.
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.

--
Have you read my blog lately?
Re:Uhhh... by amicusNYCL · 2013-02-05 05:34 · Score: 5, Funny

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

--
"Our two-party system is like a bowl of shit looking at itself in a mirror." - Lewis Black
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
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: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).